Physics Chapter 6 Momentum, Chapter 7 Energy, Physics Chapter 8 Rotational Motion, Chapter 10 Projectile Motion Physics, Chapter 9 Physics Gravity

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Work input=work output formula

(Force × distance)input = (force × distance)output.

Give an example of when your weight is greater than mg. Give an example of when your weight is zero.

. In an upward accelerating elevator your weight is greater than mg, in free fall your weight is 0.

A person grips the end of the wrench, 0.5 meters from the bolt, and pushes on the end in the direction of the bolt with a force of 50 N. What is the torque exerted on the bolt?

0 N × m. The torque would be 25 N m if the force were perpendicular to the wrench. Since the force is in the same direction as the wrench, there is no component of the force perpendicular to the wrench, so the torque is zero.

A person weighs 150 pounds. He is standing on a scale inside an elevator. If the elevator is free-falling downward (perhaps the cable broke), what is the reading of the scale?

0 pounds Since the person is in free-fall, his acceleration is -9.8 m/s/s and thus the only force acting on him is that of gravity.

A 150 pound person decides to move to the center of the Earth (carving out a little cavity for her house). What is the net force of gravity exerted by the Earth on this person?

0 pounds. Since there is the same amount of material in all directions, at equal distances from the person, the net force is zero.

1 N⋅m = ___

1 J

A block with a weight of 250 N is attached to a two pulley engine. Here, a rope is attached to the ceiling, loops under one pulley in which the block is attached, and then loops over a second pulley also attached to the ceiling (See Figure). A person is holding the other end of the rope and pulls downward such that the end of the rope is lowered 2 meters. How far does the block rise?

1 meter. The pulley never rises more than the other end of the rope lowers. The pulley attached to the block rises 1 meter, such that there is one meter of rope missing on either side of it going up to the ceiling.

Axis

1) straight line about which rotation takes place, 2) straight lines for reference in a graph, usually the x axis for measuring horizontal displacement and the y axis for measuring vertical displacement.

What is the ratio of escape speed from Earth to circular orbital speed? Ignore air resistance.

1.41

A boy and a girl are playing on a teeter totter. The boy is three times as massive as the girl. If the boy is sitting 0.5 meters away from the pivot point, how far away should the girl sit such that the two can sit balanced, horizontally?

1.5 m The torque goes as weight times distance, so the distance of the girl from the pivot point must be three times higher than that of the boy.

A 5-kg shark swimming at 1 m/s swallows an absent-minded 1-kg fish swimming toward it at 4 m/s. The speed of the shark after his meal is

1/6 m/s. M(Shark) v(shark) + m(fish) -v(fish) =M(shark +fish) * vfinal. Solving for vfinal then: (5*1) + (1*-4) = (5+1) vfinal. = 5-4 = 6vfinal = 1/6. Remember to set one side as a negative!

A person grips a wrench 0.2 meters away from the bolt and pulls in a direction perpendicular to the wrench with a force of 50 N. What is the torque exerted on the bolt?

10 N m Since the force is perpendicular to the wrench, the torque is given by torque = force times distance.

Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then

10 joules go to warming the bow. The total energy of the drawn bow, which includes the poised arrow is 50 joules. The arrow gets 40 joules but the remaining 10 joules warms the bow, still in the initial system.

How much work is done in lifting the 100-N block of ice a vertical distance of 2 m

100 N × 2 m = 200 J.

What is the efficiency of a machine that miraculously converts all the input energy to useful output energy?

100%

kilo

1000

kilowatt (kW)

1000 watts

Escape speed from Earth is any speed equal to or greater than __________.

11.2 km/s

A person weighs 150 pounds. He steps in an elevator and stands on a scale. If the elevator is moving upwards with a constant speed, what is the reading of the scale?

150 pounds. Since the elevator is not accelerating, the scale provides an upward force equal in magnitude to the force of gravity.

The mass of a ball moving at 3 m/s with a momentum of 48 kg m/s is

16 kg. Because momentum = mass * speed. If 48 kg *m/s = 3m/s * xkg. Then 48/3 = 16kg.

A block with a weight of 250 N is attached to a rope, which is draped over an elevated pulley. A person is holding the other end of the rope and raises the block by pulling down on the rope. If her hands pull the rope downward a distance of 2 meters, how high does the block rise?

2 meters. Since there is only pulley, the distance one end of the rope rises is equal to the distance the other end lowers.

Show that 2.4 J of work is done when a force of 2.0 N moves a book 1.2 m.

2 × 1.2 = 2.4J

Calculate the work done when a 20-N force pushes a cart 3.5 m.

20 × 3.5 =70 J

How much work is needed to lift a bag of groceries that weighs 200 N to a height of 3 m?

200 N × 3 m = 600 J

In an ideal pulley system, a woman lifts a 100 N crate by pulling a rope downward with a force of 25 N. For every 1 meter length of rope pulled downward, the crate rises:

25 centimeters. Work in = work out; Fd in = Fd out. One fourth of 1 m = 25 cm.

A ladybug sits halfway between the rotational axis and the outer edge of the turntable. When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge.

4 cm/s. Rotational speed of both bugs is the same, so if radial distance doubles, tangential speed also doubles. Tangential speed = rω. 2 cm/s * 2 = 4 cm/s

Consider the video. (A ball is spring loaded into a cart and launched while in motion. The ball lands inside the cart). Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment?

4 times. The ball spends twice as long in the air. From d = ½gt², and 2² = 4. The distance itself will be 4 times as great. T is the only variable that we are changing.

A cannon, sitting on the ground in a flat horizontal field, fires a cannonball. For what angle between the orientation of the cannon and the ground will the cannonball land the furthest away from the cannon? Ignore air resistance

45 degrees. At this angle, the cannonball initially has the same horizontal and vertical velocities. If the angle were larger, it would stay in the air longer but wouldn't travel as far since its horizontal speed would be smaller. If the angle were smaller, it wouldn't stay in the air as long, so even though its horizontal speed would be faster, it wouldn't get as far before hitting the ground.

A projectile falls beneath the straight-line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling for 1 s? For 2 s?

5 m, 20 m. From d = ½gt²

A girl throws a ball horizontally. As the ball leaves the girl's hand, 1 second later it will have fallen:

5 meters below the horizontal component. Whatever the speed, the ball will fall a vertical distance of 5 meters below the horizontal component.

A weightlifter exerts an upward force on a 1000-N barbell and lifts the barbell 1 meter upward in 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?

500 watts.

If an input of 100 J in a pulley system increases the potential energy of a load by 60 J, what is the efficiency of the system?

60%

Neglecting air drag, a ball tossed at an angle of 30° with the horizontal will go as far downrange as one that is tossed at the same speed at an angle of what?

60°. Horizontal distances will be the same for launching angles that add up to 90°. So 90-30 =60

What speed is required to obtain a circular orbit around the Earth?

8 km/s.

1 watt = ___ J

= 1 J/S

At what part of its trajectory does the baseball have a minimum speed?

A ball's minimum speed occurs at the top of its trajectory. If it is launched vertically, its speed at the top is zero. If launched at an angle, the vertical component of velocity is zero at the top, leaving only the horizontal component. So the speed at the top is equal to the horizontal component of the ball's velocity at any point.

Which undergoes the greatest change in momentum: A) a baseball that is caught, B) a baseball that is thrown, or C) a baseball that is caught and then thrown back, if all of the baseballs have the same speed just before being caught and just after being thrown?

A baseball that is caught then thrown back.

fuel cell

A device that converts chemical energy to electrical energy, but unlike a battery is continually fed with fuel, usually hydrogen.

What is a gravitational field, and how can its strength be measured?

A gravitational field is a force field about any mass, and can be measured by the amount of force on a unit of mass located in the field. Typically measured as newtons per kilogram.

Can a machine multiply input force? Input distance? Input energy?

A machine can multiply input force or input distance, but NEVER input energy.

What exactly is a projectile?

A projectile is any object is projected by some means and continues in motion by its own inertia.

Geosynchronous orbit

A satellite orbit in which the satellite orbits Earth once each day. When moving westward, the satellite remains at a fixed point - about 36,000 k, above earth's surface.

Which will have the greater acceleration rolling down an incline: a hoop or a solid disk?

A solid disk will. Both will rotate about the central axis and the shape that has the most of its mass far from its axis is the hoop. Therefore, it has greater rotational inertia and is harder to start rolling.

mechanical equilibrium

A state in which an object is not accelerating. Where ∑t=0.

How much time does it take for a complete revolution of a satellite in close orbit about the Earth?

About 90 minutes.

A moving object has: momentum. energy. speed. all of the above.

All of the above.

Three people are standing on a spinning merry-go-round. Person A is standing near the center, person B is standing halfway between the center and the edge, and person C is standing near the edge. Which person takes the longest amount of time to complete one circle?

All three complete the circle in the same amount of time. This means that person C is moving the fastest since he covers a larger circumference than the others.

Four pictures are shown depicting segments of equal areas, of a comet's elliptical orbit around the sun. How would we find the length of time it takes for the comet to cover each segment?

Although Kepler wrote his laws specifically to describe the orbits of the planets around the Sun, they apply more generally. Kepler's second law tells us that as an object moves around its orbit, it sweeps out equal areas in equal times. Because all the areas shown here are equal, the time it takes the comet to travel each segment must also be the same.

A projectile is launched upward at an angle of 70° from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away?

An angle of 20° because these angles sum to 90°.

What is the relationship between impulse and momentum

An impulse indicates a change in momentum. Impulse = change in momentum. Ft = ∆(mv)

What is the law of inertia for rotating systems in terms of angular momentum?

An object in rotational motion will maintain the same angular momentum unless it is acted upon by a torque.

Distinguish between linear momentum and angular momentum.

Angular momentum depends on the distribution of mass, whereas linear momentum depends on the total mass.

Projectile

Any object that moves through the air or through space, acted on only by gravity, and air resistance, if any. Due to gravity, projectiles have curved paths.

What would be the magnitude of the gravitational field anywhere inside a hollow, spherical planet?

Anywhere inside a hollow planet the gravitational field of the planet is zero.

Centrifugal force.

Apparent outward force on a rotating or revolving body

fD = Fd

Applied force x applied distance = output force x output distance. A small force applied over a long distance results in a large force moving over a short distance.

As distance increases between most of the mass of an object and its center of rotation, does rotational inertia increase or decrease?

As distance increases between most of the mass of an object from the center, rotational inertia increases. The greater the rotational inertia the greater the difficulty in changing its rotational state. For example a barbell is harder to rotate versus a dumbbell.

If a machine multiplies force by a factor of 4, what other quantity is diminished, and by how much?

As force is increased, distance is decreased by the same factor. So in this case, it decreases to a 1/4.

slows down as it approaches the event horizon, and never actually crosses the event horizon

As the falling rocket plunges toward the event horizon, an observer in the orbiting rocket would see that the falling rocket __________.

Why are all tides greatest at the time of a full Moon or new Moon?

At full moon and new moon the tides from the Moon and the Sun add because they are in line with Earth.

The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance.

Before the plane is directly over the target. At the moment it is released, the crate shares the plane's horizontal velocity. In the absence of air resistance, the crate would remain directly below the plane as it fell.

A red ball rolls off an elevated platform with an initial horizontal velocity of 2 m/s. Just as it rolls off the platform, a blue ball is dropped from the platform from rest. Which ball hits the ground first (assume the ground is horizontal and flat)?

Both balls hit the ground at the same time. Both balls have the same initial velocity in the vertical direction and experience the same acceleration. This means they will fall at the same rate and hit the ground at the same time.

A t the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which ball, the one fired downrange or the one dropped from rest, strikes the ground first?

Both hit the ground at the same time.

How can gravity be simulated in an orbiting space station?

By either rotating the space station or accelerating the space station linearly. The rotation method is sustainable for longer and it gives people in the station the illusion that gravity is pulling them towards the outside of the space station.

Is the sum of kinetic and potential energies a constant for satellites in circular orbits, in elliptical orbits, or in both?

By the law of energy conservation, the sum will always be constant.

centripetal force

Center-directed force that causes an object to follow a curved or circular path.

ellipse

Closed curve of oval shape wherein the sum of the distances from any point on the curve to two internal focal points is a constant.

black hole

Concentration of mass resulting from gravitational collapse, near which gravity is so intense that not even light can escape.

weightlessnes

Condition of free fall toward or around Earth in which an object experiences no support force and exerts no force on a scale.

parabola

Curved path followed by a projectile acting under the influence of gravity only

Inside a planet gravitational fields do what?

Decreases to zero. Because the pull from the mass of Earth below you is partly balanced by what is above you.

perturbation

Deviation of an orbiting object, e.g. a planet, from its path around a center of force, e.g. the sun, caused by the action of an additional center of force, e.g. another planet.

machine

Device for increasing or decreasing a force or simply changing the direction of a force

Twice as much work is done in lifting a load 2 stories instead of 1 story. Why?

Distance is twice as great

Suppose you take a sharper turn than before and halve the radius, by what factor will the centripetal force need to change to prevent skidding?

Double the force.

Suppose by pulling the weights inward, the rotational inertia of the spinning man reduces to half its value. By what factor would his angular velocity change?

Double. Angular momentum = rotational inertia * angular velocity. Angular momentum is proportional to rotational inertia. If you halve the rotational inertia to keep the angular momentum constant, the angular velocity would double.

An ice skater is spinning while holding her arms out perpendicular to her body. As she brings her arms towards her body, the rotational speed

Due to angular momentum being conserved, the rotational speed needs to increase if the moment of inertia decreases.

A stone is thrown upward at an angle. What happens to the vertical component of its velocity as it rises? As it falls?

Due to the force of gravity the velocity changes. On the way up it maintains the vertical initial speed until it gradually decreases zero (due to gravity pulling downward on the object). The object reaches a momentary zero, after which it increases in velocity in the downward direction as it falls to the ground.

How can a projectile "fall around the Earth"?

Earth is shaped in such a way that for every 8000 m tangential to the Earth's surface drops 5 m. Basically, every 8000 m there is 5 m drop. Projectiles that are falling around Earth are traveling at a speed that allows it orbit earth instead of fall into it.

efficiency formula

Efficiency = useful output energy/total power input

gravitational potential energy

Energy associated with a gravitational field, which on Earth results from the gravitational interaction of a body and Earth Potential energy (PE) then equals mass (m) times the acceleration due to gravity (g) times height (h) from a reference level such as Earth's surface. PE = mass × gravity × height

mechanical energy

Energy due to the position or the movement of something; potential or kinetic energy or a combination of both.

(7.1) When is energy most evident?

Energy is most evident when it is changing. The change from potential to kinetic energy when an object falls off a ledge, the heat coming off an engine, are both examples of when energy is being transformed.

Kinetic Energy (KE)

Energy of motion. Equal to mass multiplied by the square of the speed, multiplied by the constant 1/2. KE = ½mv²

Potential Energy (PE)

Energy of position, usually related to the relative position of two things, such as a stone and Earth gravitational PE, or an electron and a nucleus electric PE.

(7.1) Exactly what is it that enables an object to do work?

Energy, by definition, enables an object to do work.

Kinetic energy and work of a moving object are equal to what?

Equal to the work required to bring an object from rest to a particular speed or the work that object can do while being brought to rest.

How often do high tides occur?

Every 12 hours

What is required to change the angular momentum of a system?

External torque

An ostrich egg of mass m is tossed at a speed v into a sagging bed sheet and is brought to rest in a time t. If the mass of the egg is 0.80 kg , its initial speed is 2.4 m/s , and the time to stop is 0.20 s, find the average force on the egg.

F = (.80 * .20) ÷ .20 Force = 9.6 N.

law of universal gravitation formula

F = G(m₁m₂/d²)

centripetal force formula

F = mv²/r

True or false: Space vehicles orbit at altitudes in excess of 150 km to be above both gravity and Earth's atmosphere.

False. What satellites are above is the atmosphere and air resistance—not gravity! It's important to note that Earth's gravity extends throughout the universe in accord with the inverse-square law

True or false: Space vehicles orbit at altitudes in excess of 150 km to be above both gravity and Earth's atmosphere.

False. What satellites are above is the atmosphere and air resistance—not gravity! It's important to note that Earth's gravity extends throughout the universe in accord with the inverse-square law.

Show that about 786 W of power is expended when a 500-N barbell is lifted 2.2 m above the floor in 1.4 s.

Find work. W = force × distance. = 500N × 2.2m = 1100 J Find Power. P = Work / time = 1100J/1.4s = 786 watts

What is the relationship between the center of gravity and the support base for an object that is in stable equilibrium?

For an object in stable equilibrium the support base is placed at the center of gravity in order to balance the torques applied to the object by gravity.

law of universal gravitation

For any pair of objects, each particle attracts the other object with a force that is directly proportional to the product of the masses of the objects, and inversely proportional to the square of the distance between them, or their centers of mass if spherical objects, where F is the force, m is the mass, d is distance and G is the gravitation constant.

Impulse formula

Force × time = m∆v

Suppose you double the speed at which you round a bend in the curve, by what factor must the centripetal force change to prevent you from skidding?

Four times.

Consider an imaginary miracle car that has a 100%-efficient engine and burns fuel that has an energy content of 40 MJ per liter. If the total of air drag and overall frictional forces on the car traveling at highway speed is 500 N, how far can the car travel per liter of fuel at this speed?

From the definition work = force × distance, simple rearrangement gives distance = work/force. If all 40 million J of energy in 1 L is used to do the work of overcoming the air drag and frictional forces, the distance is (This is about 190 mi/gal.) The important point here is that, even with a hypothetically perfect engine, there is an upper limit of fuel economy dictated by the conservation of energy.

What is the magnitude of the gravitational force between two 1-kg bodies that are 1 m apart?

G = 6.67 × 10-¹¹Nm²/kg² which = 0.0000000000667 newton. This shows that gravity is a very weak force compared with electrical forces.

Einstein's Theory of Relativity

Gravitational field is a warping of space-time by a planet. The warped space time affects motion of other objects.

Why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn't change?

Gravitational force does not act horizontally. Gravity only affects the velocity of something vertical.

Show that when a 3.0-kg book is lifted 2.0 m its increase in gravitational potential energy is 60 J.

Gravitational potential energy = weight × height: PE =mgh. (3kg)(2m)(10 m/s²) = 60 J

If there is an attractive force between all objects, why don't we feel ourselves gravitating toward massive buildings in our vicinity?

Gravity certainly does pull us toward massive buildings and everything else in the universe. The forces between buildings and us are relatively small because their masses are small compared with the mass of Earth. The forces due to the stars are extremely tiny because of their great distances from us. These tiny forces escape our notice when they are overwhelmed by the overpowering attraction to Earth. Physicist Paul A. M. Dirac, 1933 Nobel Prize recipient, put it this way: "Pick a flower on Earth and you move the farthest star!"

A stone is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? As it falls?

Gravity only affects the vertical component. The horizontal initial speed was not zero since the stone was thrown at an angle. No other net force acts in the horizontal direction therefore it remains constant throughout the flight.

Which of the following forces is considered a conservative force? The force of tension from a rope. The force of friction due to a surface. Gravity. The force of someone pushing an object.

Gravity. The work done by the force of gravity is path independent. The forces of tension, friction, and a person pushing can change the total mechanical energy of a system and the work done by these forces is path dependent, so they are non-conservative forces.

At what part of an elliptical orbit does an Earth satellite have the greatest speed? The lowest speed?

Greatest nearest Earth; lowest furthest from Earth

For a planet of uniform density, how would the magnitude of the gravitational field halfway to the center compare with the field at the surface?

Half way to the center, the gravitational field is half that of the surface. G/2.

How is Dr. Hewitt able to break a piece of wood in his demonstration?

He moves his hand very quickly.

If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum change? By how much will her rate of spin increase? (Why do your answers differ?)

Her angular momentum will remain the same because of the conservation of momentum. Momentum before = momentum after. The rate of spin, RPM, will be double because she halved the rotational inertia and doubled her rotational velocity.

spring tide

High or low tide that occurs when the Sun, Earth, and the Moon are lined up so that the tides due to the sun and Moon coincide, making the high tides higher than average and the low tides lower than average.

A boy throws a ball from a tower 20 m down range. The vertical distance to the ground is 5 m. What is his pitching speed?

His pitching speed is the horizontal distance divided by time. Therefore v = d/t. Time is not stated, however, a 5 m drop indicates 1 second from the equation d = ½gt². Therefore, pitching speed is 20 m/s.

What did Kepler discover about the periods of planets and their distances from the Sun?

His third law. The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun. This is for all planets. This means the ratio T²/r³ is the same for all planets. So if a planet's period is known, its average orbital radial distance is calculated.

wormhole

Hypothetical enormous distortion of space and time, similar to a black hole, but opening out again in some other part of the universe.

ether

Hypothetical invisible medium that was formerly thought to be required for the propagation of electromagnetic waves and thought to fill space through the universe.

Rotational inertia of simple pendulum.

I = mr²

(7.2) Two cars are raised to the same elevation on service-station lifts. If one car is twice as massive as the other, compare their gains of potential energy.

If both cars are the same height but one is twice as heavy, then its potential energy would be twice as much as the other car.

(7.2) A car is raised a certain distance in a service-station lift and therefore has potential energy relative to the floor. If it were raised twice as high, how much more potential energy would it have?

If the car were raised twice as high it would have twice the amount of potential energy since the height of an object is directly proportional to its potential energy.

A force of 50 N is applied to the end of a lever, which is moved a certain distance. If the other end of the lever moves one-third as far, how much force can it exert?

If the opposite end of the lever moves only 1/3rd of the original distance then the input force is 50 * 3 = 150 N of force. The lever multiplies force.

If you hang at rest by your hands from a vertical rope, where is your center of gravity with respect to the rope?

If you hang from a rope by your hands your center of gravity will be right under the rope (and about half way down your body).

An apple hanging from a limb has potential energy because of its height. If it falls, what becomes of this energy just before it hits the ground? When it hits the ground?

Immediately before the apple hits the ground, its initial PE becomes KE. When it hits the ground its energy becomes thermal energy.

Why does the force of gravity change the speed of a satellite when it is in an elliptical orbit but not when it is in a circular orbit?

In a circular orbit, the gravitational force is always perpendicular to the orbital path. With no component of gravitational force along the path, only the direction of motion changes—not the speed. In elliptical orbit, however, the satellite moves in directions that are not perpendicular to the force of gravity. Then components of force do exist along the path, which change the speed of the satellite. A component of force along (parallel to) the direction the satellite moves does work to change its KE.

efficiency

In a machine, the ratio of useful energy output to total energy input, or the percentage of the work input that is converted to work output. Efficiency = useful energy output / total energy input

What is recycled energy?

In a typical electric power generation plant, input fuel is used to create electricity while excess thermal energy, in the form of steam, is wasted in the process. Two-thirds of this energy is actually wasted. Recycled energy utilizes this energy that would be otherwise be wasted.

Satellites in close circular orbit fall about 5 m during each second of orbit. Why doesn't this distance accumulate and send satellites crashing into Earth's surface?

In each second, the satellite falls about 5 m below the straight-line tangent it would have followed if there were no gravity. Earth's surface also curves 5 m beneath a straight-line 8-km tangent. The process of falling with the curvature of Earth continues from tangent line to tangent line, so the curved path of the satellite and the curve of Earth's surface "match" all the way around the planet. Satellites do, in fact, crash to Earth's surface from time to time when they encounter air resistance in the upper atmosphere that decreases their orbital speed.

equilibrium

In general, a state of balance. For mechanical equilibrium, the state in which no net forces and no net torques act. In liquids, the state in which evaporation equals condensation. More generally, the state in which no net change of energy occurs.

A satellite is placed in orbit at the plane of Earth's equator. Why?

In order to appear motionless to an observer at a fixed location on Earth's surface, the satellite must rotate around Earth at the same rate as Earth rotates around its own axis and both the location and satellite must be in the same line between Earth's center and the satellite. a This can only occur above Earth's equator. Above any other location, the "ring" of satellite motion and the "ring" of motion of the location on Earth's surface would not be in the same plane.

What would Dr. Hewitt need to have done to exert an even greater force than he did in his karate demonstration?

Increase the change in momentum, and decrease the time duration.

Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of an automatic washing machine?

Inward force. The clothes have some velocity and they have a tendency to continue moving in whatever direction they are presently moving. This means a force inward needs to be applied to keep them from flying out while the washing machine is spinning.

How does the lever arm change when you decrease the distance to the nut?

It decreases

How does the lever arm change if you decrease the angle of the force?

It decreases.

In what sense does the Moon "fall"?

It falls away from the straight path that it would follow if there were no forces acting on it.

Predict how the vertical component of the velocity will change with time after the projectile is fired.

It first decreases to zero and then increases in the opposite direction.

What happens to the strength of the gravitational field at the surface of a star that shrinks?

It increases.

How does the thickness of paint sprayed on a surface change when the sprayer is held twice as far away?

It is 0.25 as thick.

Is it easier for a circus performer to balance a long rod held vertically with people hanging off the other end, or the same long rod without the people at the other end, and why?

It is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater.

Consider balancing a hammer upright on the tip of your finger. The head is likely heavier than the handle. Is it easier to balance with the end of the handle on your fingertip, with the head at the top, or the other way around?

It is easier to stand the handle on your finger tips and the head at the top. This way there is greater rotational inertia and it will be more resistant to rotational change.

Is it easier to balance a long rod with a mass attached to it when the mass is closer to your hand or when the mass is farther away?

It is easier when the mass is farther from your hand.

When a projectile achieves escape speed from Earth, it does what?

It outruns the influence of Earth's gravity, but is never beyond it. All objects within the universe impart some gravitational force upon each other. That does not mean that the force is strong enough for the object to return.

Predict how the horizontal component of the velocity will change with time after the projectile is fired.

It stays constant.

A ball is thrown horizontally from a cliff at a speed of 10 m/s. You predict that its speed 1 s later will be slightly greater than 14 m/s. Your friend says it will be 10 m/s. Show who is correct.

It will be slighter greater than 14 m/s. Find the resultant of the horizontal and vertical components.

If you toss a stick into the air, it appears to wobble all over the place. Specifically, about what place does it wobble?

It wobbles about it's center of mass

If Earth shrank but there was no change in its mass, what would happen to your weight at the surface?

It would increase.

If Earth shrank, but there was no change in its mass, then what would happen to your weight at the surface?

It would increase.

Which is easier to get swinging: a baseball bat held at the narrow end or a bat held closer to the massive end (choked up)?

Its easier to get a bat to swing if you hold it closer to the massive end. This is because there is greater distance at the narrow end which provides greater rotational inertia.

What will be the kinetic energy of a pile driver ram that starts from rest and undergoes a 10-kJ decrease in potential energy?

Its gain in KE will equal its decrease in PE, 10 kJ.

From Part B, you know that from afar you'll never see the in-falling rocket cross the event horizon, yet it will still eventually disappear from view. Why?

Its light will become so redshifted that it will be undetectable. As the video shows, viewed from afar the light of the in-falling rocket becomes increasingly redshifted. As it approaches the event horizon, the redshift approaches infinity, meaning all its light is stretched to such enormous wavelengths that no detector could see it, even in principle

What is rotational inertia, and how is it similar to inertia as studied in earlier chapters?

Just as discussed in earlier chapters, rotational inertia means that an object rotating about an axis tends to remain rotating about the same axis unless interfered with by some external influence.

A block with a weight of 250 N is attached to a two pulley engine. Here, a rope is attached to the ceiling, loops under one pulley in which the block is attached, and then loops over a second pulley also attached to the ceiling (See Figure). A person is holding the other end of the rope and wishes to raise the block by pulling down on the rope. What is the minimum force the person must pull down on the rope to lift the pulley?

Just over 125 N. Since the rope is pulling upwards on the pulley with a net force of two times the tension, the tension only needs to half the weight of the block to balance the force of gravity.

A block with a weight of 250 N is attached to a rope, which is draped over an elevated pulley. A person is holding the other end of the rope and wishes to raise the block by pulling down on the rope. What is the minimum force the person must pull down on the rope to lift the pulley?

Just over 250 N. The person needs to produce a tension in the rope that is at least equal to the force of gravity pulling downward on the block.

(7.4) Compared with a car moving at some original speed, how much work must the brakes of a car supply to stop a car that is moving twice as fast? How will the stopping distances compare?

KE =½mass × velocity² = Force × distance. Which is the work required to stop the vehicle. If the velocity doubles, KE becomes four times. So the work to stop is also 4 times. The stopping distance is also four times as great.

(7.3) When the speed of a moving car is doubled, how much more kinetic energy does it have?

KE =½mass × velocity². If velocity is doubled then, 2 velocity. Therefore, KE becomes 4 times if the velocity doubles.

Where does a satellite have the greatest KE? The greatest PE? The greatest total energy.

KE is maximum at the perigee, the closest point to Earth at the bottom of the track. PE is maximum at the apogee, the farthest point from Earth. The total energy is the same everywhere in orbit.

If object speed is doubled what is the KE?

KE is quadrupled. ½mv². Since velocity is squared, twice the speed would be 4 times the speed.

kinetic energy formula

KE=½mv².

What was the direction of the force on a planet in Kepler's thinking? In Newton's thinking?

Kepler did not appreciate the concept of inertia. He believed that force on a moving body would be in the same direction as the body's motion. Newton realized that it is gravity that pulls objects toward each other.

Four pictures are shown depicting segments of equal areas, of a comet's elliptical orbit around the sun. How would we find and rank the distance the comet travels between each segment?

Kepler's second law tells us that the comet sweeps out equal areas in equal times. Because the area triangle is shorter and squatter for the segments nearer to the Sun, the distance must be greater for these segments in order for all the areas to be the same.

inverse-square law

Law relating the intensity of an effect to the inverse square of the distance from the cause. Gravity, electric, magnetic, light, sound, and radiation phenomena follow the inverse-square law. Intensity ~ 1/distance²

A bag of groceries that weighs 200 N is lifted to a height of 3 m. How much work is needed to lift the bag twice as high?

Lifting the bag twice as high requires twice the work (200 N × 6 m = 1200 J

Where is the center of mass of Earth's crust?

Like a giant basketball, Earth's crust is a spherical shell with its center of mass at Earth's center.

Can we correctly say that hydrogen is a new source of energy? Why or why not?

Like electricity, hydrogen is a carrier of energy, not a source. That's because it takes energy to separate hydrogen from molecules.

tangent

Line that touches a curve in one place only and is parallel to the curve at that point.

RPM

Means revolutions per minute.

In which is momentum conserved: an elastic collision or an inelastic collision?

Momentum is conserved for both. Net mv(before) = Net mv (after)

How is a flywheel constructed to maximize its rotational inertia?

Most of the mass is concentrated far from the axis.

Newton viewed the curving of the path of a planet as being caused by a force acting on the planet. How did Einstein view the curved path of a planet?

Moving in curved 4-dimensional spacetime

What was the cause of perturbations discovered in the orbit of the planet Uranus? What greater discovery did this lead to?

Neptune caused the perturbations, and later Pluto was discovered.

Can a machine multiply energy?

Never. It can multiply force but not energy.

What did Newton discover about gravity?

Newton discovered that gravity is directly proportional to the product of two masses and inversely proportional to the square of the distance separating them.

Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn't a heavy body fall faster than a light body?

Newton's second law (a = F/m) reminds us that greater force acting on greater mass does not result in greater acceleration.

When you are driving at 90 km/h, how much more distance do you need to stop compared with driving at 30 km/h?

Nine times more. The car has 9 times as much kinetic energy when it travels three times as fast: ½m(3v)² = ½m9v² = 9(½mv²). The friction force will ordinarily be the same in either case; therefore, 9 times as much work requires 9 times as much distance.

Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was moving upward at constant velocity? Downward at constant velocity?

No changes in compression when moving at constant velocity.

If you are not wearing a seat belt in a car that rounds a curve, and you slide across your seat and slam against a car door, what kind of force is responsible for your slide: centripetal, centrifugal, or no force? Why is the correct answer "no force"?

No force causes you to slam into your car door. It is natural to continue moving in a straight line unless you are acted upon by a force.

If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight-line path: centripetal, centrifugal, or no force? What law of physics supports your answer?

No force. The can is already in motion, by the law of inertia, it will keep moving until acted upon by an external force.

Is the following explanation valid? Satellites remain in orbit instead of falling to Earth because they are beyond the main pull of Earth's gravity.

No, If any moving object were beyond the pull of gravity, it would move in a straight line and would not curve around Earth. Satellites remain in orbit because they are being pulled by gravity, not because they are beyond it. For the altitudes of most Earth satellites, Earth's gravitational field is only a few percent weaker than it is at Earth's surface.

Can an object have more than one momentum at a given moment?

No, an object always has one unique velocity and one unique mass at any given moment.

Consider an apple at the top of a tree that is pulled by Earth's gravity with a force of 1 N. If the tree is twice as tall, will the force of gravity be 1/4 as strong? Defend your answer.

No, because an apple at the top of the twice as tall apple tree is not twice as far from Earth's center. The taller tree would need a height equal to Earth's radius (6370 km) for the apple's weight at its top to reduce to 1/4 N , we disregard the effects of everyday changes in elevation..

When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor?

No, both are the same. the momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended.

Does a moving object have impulse?

No, impulse is not something an object has, like momentum. Impulse is what an object can provide or what it can experience when it interacts with some other object. An object cannot possess impulse just as it cannot possess force.

Can an object have more than one center of gravity?

No. A rigid object has one CG. If an object is nonrigid, such as a piece of clay or putty, and is distorted into different shapes, then its CG may change as its shape changes. Even then, it has one CG for any given shape

Do your answers to the preceding question depend on the angle at which the projectile is launched?

No. Gravity always acts downward. At some point a projectile will reach it's maximum height, reach a momentary velocity of zero, and then begin falling back down with increased velocity.

We know that both the Moon and the Sun produce our ocean tides. And we know that the Moon plays the greater role because it is closer. Does the Moon's closeness mean that it pulls on Earth's oceans with a greater gravitational force than the Sun?

No. The Sun's pull is much stronger. But the difference in lunar pulls is greater than the difference in solar pulls. So our tides are due primarily to the Moon

Can an object have work?

No. Unlike momentum or energy, work is not something that an object has. Work is energy in transit. It is the energy transferred when a force acts on an object as it moves through a distance.

Would a torque on the Moon occur if the Moon were spherical, with both its center of mass and center of gravity in the same location?

No. the torque requires a distance between the center of mass and the center of gravity. There is no lever arm between Earth's gravitational pull and the Moon's axis.

Now, consider the collision between two happy balls described in Part A. How much of the balls' kinetic energy is dissipated?

None of it. In this scenario, since the collision between the happy balls is elastic, the kinetic energy will be conserved, and thus none will be dissipated.

What would happen to Earth if the Sun became a black hole?

Nothing, actually. Letting the equation for gravity guide our thinking, we see that no mass changes, no distance from center to center changes, so there would be NO change in force between the Sun an Earth.

What is the ultimate source of geothermal energy?

Nuclear energy from the Earth's inner layers beneath the crust. Geothermal energy is mostly used in areas that have volcanic activity or areas in which the Earth's mantle can bypass the crust and go onto the surface of our planet.

Do tides depend more on the strength of gravitational pull or on the difference in strengths? Explain.

Ocean tides are caused by differences in pulling strengths.

For an Earth satellite in circular orbit, list all the values that do not change.

Only speed, gravitational force, and distance from Earth

For orbits of greater altitude, is the period longer or shorter?

Orbital speed is less, the distance is greater, and the period is longer.

Show that 50 W of power is required to give a brick 100 J of PE in a time of 2 s.

P = work / time P = 100 J / 2 s = 50 Watts.

gravitational potential energy formula

PE = mass × gravity × height

linear speed

Path distance moved per unit of time. Also just called speed.

lever arm

Perpendicular distance between an axis and the line of action of a force that tends to produce rotation about that axis.

Fulcrum

Pivot point of a lever.

center of mass

Point at the center of an object's mass distribution, where all its mass can be considered to be concentrated. For everyday conditions, it is the same as the center of gravity.

center of gravity

Point at the center of the object's weight distribution, where the force of gravity can be considered to act.

Perigee

Point in an elliptical orbit closest to the focus about which orbiting takes place.

apogee

Point in an elliptical orbit farthest from the focus around which orbiting takes place.

(7.2) When is the potential energy of something significant?

Potential energy of an object is significant when it changes into another form of energy, such as kinetic energy, heat transfer, or mechanical energy.

(7.1) If both sacks in the preceding question are lifted their respective distances in the same time, how does the power required for each compare? How about for the case in which the lighter sack is moved its distance in half the time?

Power is defined by work divided by time. If the two in the previous question have the same value for work and time then the power of the two scenarios would also be the same. If the lighter sack is moved the same distance as the heavier sack in half the time the power of that scenario would be twice as much since the time would have been halved.

When a car rounds a curve, the centripetal force prevent it from what?

Prevents it from skidding off the road. If the road is wet or if the car is going to fast, the centripetal force is insufficient to prevent skidding off the road.

conservation of energy

Principle that energy cannot be created or destroyed. It may be transformed from one form into another, but the total amount of energy never changes.

Angular momentum

Product of a body's rotational inertia and rotational velocity about a particular axis. For an object that is small compared with the radial distance, it is the product of mass, speed, and radial distance of rotation. Angular momentum = mass × velocity × radial distance.

torque

Product of force and lever-arm distance, which tends to produce rotational acceleration. Torque - lever-arm distance × force

impulse

Product of force and the time interval during which the force acts. Impulse produces change in momentum. Impulse = Ft = ∆(mv)

Work (W)

Product of the force on an object and the distance through which the object is moved, when force is constant and motion is in a straight line in the direction of the force. Measured in joules. Work = force x distance.

linear momentum

Product of the mass and the velocity of an object. Also called momentum. This definition applies at speeds much less than the speed of light.

Satellite

Projectile or smaller celestial body that orbits a larger celestial body

Power

Rate at which work is done or energy is transformed, equal to the work done or energy transformed divided by time; measured in watts. Power = work/time

mechanical advantage

Ratio of output force to input force for a machine.

Relative

Regarded in relation to something else, depending on point of view or frame of reference. Sometimes referred to as "with respect to".

Rotational inertia

Reluctance or apparent resistance of an object to change its state of rotation, determined by the distribution of the mass of the object and the location of the axis of rotation or revolution.

Why is it advantageous to roll with the punch in boxing?

Rolling with the punch increases contact time, which decreases the force.

Inertia depends on mass; rotational inertia depends on mass and something else. What?

Rotational inertia depends on the distribution of the mass about the axis of rotation. The greater the distance between an object's mass concentration and the axis the greater the rotational inertia.

Why does the rotational inertia of the rod with the attached mass closer to your hand compare the way it does with the rotational inertial of the rod with the attached mass farther away?

Rotational inertia depends on whether the mass is farther or closer to the point of rotation. The farther the mass is, the higher the rotational inertia.

On a rotating turntable, does tangential speed or rotational speed vary with distance from the center?

Rotational speed does not vary with distance. Rotational speeds is the measurement of revolutions per unit of time. Tangential speed depends on radial distance. It is measured as: Tangential speed ~ radial distance × rotational speed. v~rw

Rotational velocity

Rotational speed together with a direction for the axis of rotation or revolution.

watt

SI unit of power. One watt is expended when 1 joule of work is done in 1 second. 1 W = 1 J/s.

Consider the balanced seesaw in Figure 8.18. Suppose the girl on the left suddenly gains 50 N, such as by being handed a bag of apples. Where should she sit in order to be in balance, assuming the heavier boy does not move?

She should sit ½ m closer to the center. Then her lever arm is 2.5 m. This checks: 300 N × 2.5 m = 500 N × 1.5 m.

lever

Simple machine made of a bar that turns about a fixed point called the fulcrum.

Imagine a ladybug sitting halfway between the rotational axis and the outer edge of the turntable in Figure 8.1b. When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge?

Since all parts of the turntable have the same rotational speed, her friend also rotates at 20 RPM. Tangential speed ~ radial distance × rotational speed. Since the friend is twice as far from the axis of rotation, she moves twice as fast—4 cm/s.

Railroad car A rolls at a certain speed and makes a perfectly elastic collision with car B of the same mass. After the collision, car A is observed to be at rest. How does the speed of car B compare with the initial speed of car A?

Since the cars have the same mass, Car B must have the same velocity as Car A did by conservation of momentum.

Suppose a ball of putty moving horizontally with 1 kg⋅m/s of momentum collides with and sticks to an identical ball of putty moving vertically with 1 kg⋅m/s of momentum. What is the magnitude of their combined momentum?

Since the two masses stick together, they will move at a diagonal direction of 45°, at a rate of √2 kg⋅m/s

Why is it important that the projectile in the preceding question be above Earth's atmosphere?

So air resistance or another friction force does not act upon the object. This way velocity is not slowed down and the object could not come crashing down.

Photovoltaic cells

Solar cells. Initially they were crystal wafers produced the same way that semiconductors are made for computers, or as thin coatings on glass or metal backing. Light and flexible photovoltaic power sheets are as thick as aluminum foil and can be mounted almost anywhere.

Playing in the rain, a little girl tackles a little boy. Just before she tackles him, the boy is running east at 3 m/s and the girl is running south at 4 m/s. After the tackle, the girl holds on and the two slide on the wet grass. Our system consists of just the two children. Before the tackle, in roughly what direction does the total momentum of the system point?

Somewhere south of east, but we can't be any more specific than that because the mass of the children are not specified. If one is larger than the other it would affect the momentum of the tackle.

For an Earth satellite in an elliptical orbit, list all the values that do change.

Speed, gravitational force, and distance from Earth

Rotation

Spinning motion that occurs when an object rotates about an axis located within the object, usually an axis through its center of mass.

Which has the higher tides: spring tides or neap tides?

Spring tides are higher, because the tides from the Moon and Sun add together.

Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward? Downward?

Springs are more compressed when accelerating upward, and less compressed when accelerating downward.

unstable equilibrium

State of an object balanced so that any small displacement or rotation lowers its center of gravity.

stable equilibrium

State of an object balanced so that any small displacement or rotation raises its center of gravity.

linear motion

Straight-line motion, as opposed to circular, angular, or rotational motion.

period of satellite motion formula

T = 2π ×√distance³ / gravity × mass. G is the universal gravitational constant, M is the mass of Earth (or whatever body the satellite orbits), and d is the distance of the satellite from the center of Earth or other parent body.

What are the units of measurement for tangential speed? For rotational speed?

Tangential speeds is measured in meters per second. mwh/s. Rational speed is measured as the number of rotations per unit of time. Typically expressed as revolutions per minute or RPM.

engineering

Technology directed to the design, construction and maintenance of works, machinery, roads, railways, bridges, engines, all manner of vehicles from micro-carts to space stations, and to the generation, transmission, and use of electrical power. Some main divisions are aerospace, chemical, civil, communication, electrical, electronic, materials, mechanical, mining, and structural.

inelastic

Term applied to a material that does not return to its original shape after it has been stretched or compressed.

conserved

Term applied to a physically quantity such as momentum, energy, or electric charge, that remains unchanged during interactions.

energy

That which can change the condition of matter. Commonly defined as the ability to do work; actually only describable by examples.

force field

That which exists in the space surrounding a mass, electric charge, or magnet, so that another mass, electric charge, or magnet introduced into this region will experience a force. Examples of force fields are gravitational fields, electric fields, and magnetic field.

A hoop and a disk are released from the top of an incline at the same time. Which one will reach the bottom first?

The Disk. The hoop has a larger rotational inertia so it will be slower in gaining speed.

Why doesn't the Leaning Tower of Pisa topple over?

The Leaning Tower of Pisa does not topple over because its center of mass is over its base. If its center of mass was not above its base then it would tip over, unless the ground somehow provided a counter-torque.

Two blocks are attached on either side of a pulley. Block A has a mass of m and Block B has a mass of 2m and is lower than Block A. Which of the following statements correctly describes the system shown in the figure?

The angular acceleration of the pulley is nonzero.

Does an automobile consume more fuel when its air conditioner is turned on? When its lights are on? When its radio is on while the motor is turned off in the parking lot?

The answer to all three questions is yes because all the energy consumed ultimately comes from the fuel. Even the energy taken from the battery must be given back to the battery by the alternator, which is turned by the engine, which runs from the energy of the fuel.

Why is a force that is applied for a short time more effective in karate?

The average force is increased. A force that is applied for a short time is able to deliver a high impact force for the same change in momentum. If the time is small the force will be greater Ft=mv.

Two balls are thrown at the same time. One is thrown horizontally, the other is dropped. They both land at the same time. Which ball has the greatest speed at the moment of impact?

The ball thrown horizontally. The two balls have the same vertical velocity when they land, but the thrown ball has an additional horizontal velocity component. Since speed is defined as the magnitude of the resultant velocity vector, the thrown ball is moving faster when it lands.

A 100-N block of ice is lifted a vertical distance of 2 m. What is the increase in the block's gravitational potential energy.

The block is lifted upward therefore the work done = the potential energy which is 200 j.

If that same car is powered by a 25%-efficient engine, how far can it travel at highway speed on 1 liter of fuel?

The car was able to travel 80 km/L. If the engine is only 25% efficient it'd only go ¼ as far. So 20 km/L of fuel.

In terms of center of gravity, support base, and torque, why can't you stand with your heels and back to a wall and then bend over to touch your toes and return to your stand-up position?

The center of gravity moves when you move forward so the center of gravity isn't in line with the support base. So when you're against a wall you tip over.

Where is the center of mass of a baseball? Where is its center of gravity? Where are these centers for a baseball bat?

The center of mass and center of gravity for a baseball are in the center - the mass is distributed uniformly in spherical objects. The center of mass and gravity for a baseball bat is on the heavier side.

Where is the center of mass of a hollow soccer ball?

The center of mass of a soccer ball is in the center of the ball (in the core). This is because a soccer ball is spherically symmetric.

Two blocks are attached on either side of a pulley. Block A has a mass of m and Block B has a mass of 2m and is lower than Block A. What happens when block B moves downward.

The cord's tension on the right side of the pulley is higher than on the left side. If the pulley were stationary (as in many systems where only linear motion is studied), then the tension in the cord on both sides of the pulley would be equal; however, if the pulley rotates with a certain angular acceleration, as in the present situation, the tensions must be different. If they were equal, the pulley could not have an angular acceleration.

(7.4) If you push a crate horizontally with 100 N across a 10-m factory floor and the friction between the crate and the floor is a steady 70 N, how much kinetic energy does the crate gain?

The crate moves across 10 meters when you push it with 100 Newtons of force. There is a frictional force of 70 Newtons between the crate and the floor. Kinetic energy gained by the crate is going to equal the amount of work done. Work = ∆KE. (100 N - 70 N)(10 m) = (30 N)(10 m) = 300 Nm = 300 J. The amount of work done is equal to the net force multiplied by the distance. So the crate moves with a net force of 30 Newtons across 10 meters which equals 300 Newton meters or 300 joules.

Suppose you weigh 400 pounds and want to weigh only 100 pounds. Instead of going on a diet, you could live in space. How far from the center of the Earth would you have to live?

The distance would be two Earth radii away from the center of the Earth. Since the distance to the center of the Earth doubled, the weight would decrease by a factor of four.

As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?

The elevator moves downward while slowing in speed.

Why is a black hole invisible?

The escape velocity of the black hole is greater than the speed of light

Why does the force of gravity change the speed of a satellite in an elliptical orbit?

The farther the object is from Earth the weaker the force of gravity is. As an object orbits away from Earth its speed decreases. On the return to Earth the speed increases which propels it around the surface and back up again.

Why is it dangerous to slide open the top drawers of a fully loaded file cabinet that is not secured to the floor?

The file cabinet is in danger of tipping because the center of gravity may extend beyond the support base. If it does, then torque due to gravity tips the cabinet.

Why do both the Sun and the Moon exert a greater gravitational force on one side of Earth than on the other?

The force between the Moon and Earth is stronger on the side facing the Moon. The gravitational force is weaker with increased distance.

How does the force of gravity between two bodies change when the distance between them is doubled?

The force decreases to 1/4 of its initial value.

By how much does the gravitational force between two objects decrease when the distance between their centers is doubled? Tripled? Increased tenfold?

The force decreases to 1/4, 1/9, and 1/100 the original value. Because gravitational force = 1/d²

What is the magnitude of Earth's gravitational force on a 1-kg body at Earth's surface?

The force is about 10 N, or 9.8 N precisely

For the same force, why does a long cannon impart more speed to a cannonball than a short cannon?

The force is applied for a longer time in the long cannon.

Why doesn't the force of gravity change the speed of a satellite in circular orbit?

The force is at a right angle to the velocity. Gravity only pulls down ward. The satellite only moves in a direction perpendicular to the force of gravity that acts on it. It does not move in the direction of the force, otherwise speed would increase. There is no force to move an object forward or backward. Therefore, gravity is only pulling the satellite along its curves.

State Newton's law of universal gravitation in words. Then do the same with one equation.

The force is proportional to the product of two masses and inversely proportional to the square of the distance between their centers. As an equation: F ~ m₁ ×m₂/d²

Twice as much work is done in lifting 2 loads 1 story high versus lifting 1 load the same vertical distance. Why?

The force needed to lift twice the load is twice as much

When helping a friend move into a new home, you push a chair across the room. What do you know about the force of gravity applied to the chair?

The force of gravity applied to the chair does not change the energy of the system (the chair) and therefore does no work on the system.

Why is kinetic energy a constant for a satellite in a circular orbit but not for a satellite in an elliptical orbit?

The force of gravity is perpendicular to the motion in a circular orbit but not in an elliptical orbit.

What occurs when there is less time in an impulse?

The force of impact is large.

If a boxer is able to increase the duration of impact to three times as long by riding with the punch, by how much will the force of impact be reduced?

The force of impact will be only a third of what it would have been if he hadn't pulled back.

If the boxer instead moves into the punch so as to decrease the duration of impact by half, by how much will the force of impact be increased?

The force of impact will be two times greater than it would have been if he had held his head still. Impacts of this kind account for many knockouts.

weight

The force that an object exerts on a supporting surface, or if suspended, a supporting string. Often, but not always, due to the force of gravity.

When helping a friend move into a new home, you push a chair across the room. What do you know about the force that you exert on the chair?

The force you exert on the chair contributes to the overall change in kinetic energy of the system (the chair) with a positive amount and therefore does positive work on the system.

When helping a friend move into a new home, you push a chair across the room. What do you know about the force of friction applied to the chair by the floor?

The frictional force applied to the chair contributes to the overall change in kinetic energy of the system (the chair) with a negative amount and therefore does negative work on the system. We can think of work as the transfer of energy to or from a body by the application of a force. Since the frictional force applied to the chair is in the opposite direction to the displacement of the chair, then the work done by that force is negative and helps to decrease the chair's kinetic energy.

A block slides along a rough surface and comes to a stop. What can you conclude about the frictional force exerted on the block?

The frictional force does negative work on the block and decreases its kinetic energy. The frictional force acting on the block points in the opposite direction to the displacement of the block, so by definition the work is negative. And, according to the work-energy theorem, the work done is equal to the change in kinetic energy. A negative change in kinetic energy means that the kinetic energy decreases.

Halfway to the center of Earth, would the force of gravity on you be less than at the surface of Earth?

The gravitational force on you would be less because there is less mass of Earth below you, which pulls you with less force. If Earth were a uniform sphere of uniform density, the gravitational force halfway to the center would be exactly half that at the surface. But since Earth's core is so dense (about seven times the density of surface rock), the gravitational force halfway down would be somewhat more than half. Exactly how much depends on how Earth's density varies with depth, which is information that is not known today.

How does the gravity in the Space Shuttle compare with the gravity on Earth's surface?

The gravity in the Space Shuttle is approximately equal to the gravity on the surface of the Earth.

The diameter of the base of tapered cup is 6 cm. The diameter of the mouth is 9 cm. The path of cup curves when you roll it. Which end, the base or the mouth, rolls faster. How much faster?

The greater the radius or diameter, the greater the tangential speed. So the wide part rolls faster. 9/6 = 3/2 = 1.5 times faster

A ball is thrown from the ground with a 45 degree angle between the initial velocity and the horizontal ground. When the ball reaches its highest point above the ground,

The horizontal component of the velocity and the acceleration of the ball are the same as right after the ball was thrown. The acceleration is always that of gravity. If it were zero, then the ball would move in a straight line from that location. There is no acceleration in the horizontal direction, so the horizontal speed doesn't change. Also, the acceleration is solely due to gravity, which doesn't change throughout the trajectory.

A red ball rolls off an elevated platform with an initial horizontal velocity. As it is falling down, how does the horizontal component of its velocity change (ignore air resistance)?

The horizontal component of the velocity does not change as the ball falls. Since the acceleration of the ball is solely due to gravity, which points directly downward, there is no acceleration in the horizontal direction.

How will the impulse resulting from the impact differ if her hand bounces back upon striking the bricks?

The impulse will be greater if her hand bounces from the bricks upon impact. If the time of impact is not correspondingly increased, a greater force will then be exerted on the bricks (and her hand!).

What is meant by the "lever arm" of a torque?

The lever arm about any axis of rotation is the perpendicular distance from the axis to the line along which the force acts. Therefore, it is the shortest distance between the applied force and the rotational axis. Torque is defined as the product of the lever arm and the force that produces rotation: Torque = lever arm × force.

Kepler's second law

The line from the sun to any planet sweeps out equal areas of space in equal time intervals.

The magnitude of the work done by gravity is equal to the work done by the person. The magnitude of the work done by gravity is 250 N x 1 m = 250 J, the same as that done by the person.

A uniform meterstick supported at the 25-cm mark balances when a 1-kg rock is suspended at the 0-cm end. What is the mass of the meterstick?

The mass of the meterstick is 1 kg.

The minimum force required to raise the block is 125 N and that work is force time distance. The minimum force is 125 N, so work is 125 N x 2 m = 250 J.

The Moon falls around Earth rather than straight into it. If the Moon's tangential velocity were zero, how would it move?

The moon would fall into the Earth

Why are International Space Station occupants weightless when they are firmly in the grip of Earth's gravity?

The occupants are without a support force.

Kepler's First Law

The path of each planet around the Sun is an ellipse with the sun at one focus.

Suppose Earth doubled in mass. How would Earth's orbital period around the Sun change?

The period would remain one year. Kepler's third law tells us that for a planet orbiting the Sun, the planet mass does not affect the orbital period

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the potential energy stored in the spring during this motion?

The potential energy in the spring increases because the spring does negative work on the block. By definition, the change in potential energy is equal to the negative work done by the force: ∆PE = -W

A projectile is launched vertically at 100 m/s. If air resistance can be ignored, at what speed will it return to its initial level?

The projectile will return at the same speed off 100 m/s.

Universal gravitational constant

The proportionality constant G that measures the strength of gravity in the equation for Newton's law of universal gravitation. F = G(m₁m₂/d²)

(7.1) A force sets an object in motion. When the force is multiplied by the time of its application, we call the quantity impulse, and an impulse changes the momentum of that object. What do we call the quantity force multiplied by distance?

The quantity of force multiplied by distance is the work done by the force. (Work)

The question looks for distance. Use work = force × distance.

How does the rotational inertia of the rod with the mass toward the bottom compare with the rotational inertia of the mass toward the top?

The rotational inertia of the rod with the mass closer to the top is greater than the rotational inertia of the rod with the mass closer to the bottom.

What is an ellipse?

The set of points in which the combined distance from the two foci is the same. This is only true if the two foci are at the same location, which makes a special ellipse called a circle. This is why you can draw an ellipse using string, with both ends tacked to the two foci.

When Dr. Hewitt cuts the broom right through the center of gravity, how do the weights of the two sides of the broom compare?

The shorter side, where the bristles of the broom are, has a greater weight than the handle. The longer side (the handle) has a greater weight than the bristle side.

What is the source of energy in sunshine?

The source of the energy of sunshine is fusion power in the Sun.

Why do the astronauts in the Space Shuttle float around?

The space shuttle is in free fall so the shuttle and the astronauts inside it are continuously falling toward the Earth. They thus experience apparent weightlessness.

A bowling ball is in a circular orbit above the atmosphere of the Earth. Does the speed of the ball change throughout its orbit?

The speed of the ball is constant. The ball is never falling or rising away from the Earth, so its potential energy never changes. Thus its kinetic energy never changes.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the work done by the spring on the block during this motion?

The spring does negative work on the block because the spring force is in the opposite direction of the block's displacement. When a spring is compressed, the spring force pushes in the opposite direction, tending to restore the spring back to its equilibrium position. In this case, the spring force would point in the positive x-direction with the displacement of the block in the negative x-direction, resulting in a negative amount of work done by the spring force.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. The block can be pushed in the negative x-direction to compress the spring or pulled in the positive x-direction to stretch the spring. Where along the x-axis does the block have to be for the spring to have zero potential energy?

The spring has zero potential energy when the block is at x = 0, where the spring is neither stretched nor compressed. The elastic potential energy stored in a spring is a function of the deformation in the spring, x, or how much it has been stretched or compressed from equilibrium.

Kepler's Third law

The square of the orbital period of a planet is directly proportional to the cub of the average distance of the planet from the Sun, T² ~ r³ or all planets.

What is the ultimate source of energy for fossil fuels, dams and windmills?

The sun is the source for these energies. Petroleum, coal, natural gas, and wood are derivied through photosynthesis, where plants store solar energy as plant tissue. Dams rely on the water cycle to generate power. Windmills rely on wind which is caused by uneven warming of the Earth's surface.

A record player is spinning with a certain rotational speed. An ant is standing somewhere on the record without slipping. Suddenly, the rotational speed of the record player is doubled (it is spinning twice as quickly). What happens to the ant's tangential speed?

The tangential speed doubles. The ant travels around the same circle in half the time it used to take, so the tangential speed is twice as high

Tangential velocity angle of a planet or moon

The tangential velocity of a planet or moon moving in a circle is at a right angle to the force of gravity.

How does the tapered rim of a wheel on a railroad train allow one part of the rim to have a greater tangential speed than another part when it is rolling on a track?

The tapered rim means that some points of the wheel have a greater tangential speed. The wide part provides a greater speed while the narrow part has less. So, when a train rounds a curve, wheels on the outer track ride the wide part of the tapered rims, while the opposite wheels ride on the narrow parts. This way wheels have different tangential speeds for the same rotational speed. Otherwise, scraping would occur.

How does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point?

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side, and opposite in direction.

Trains ride on a pair of tracks. For straight-line motion, both tracks are the same length. Not so for tracks along a curve, however. Which track is longer: the one on the outside of the curve or the one on the inside?

The track on the outside of the curve is longer—just as the circumference of a circle of greater radius is longer.

A cannonball is fired horizontally from the top of the highest mountain on Earth with an initial velocity of 10 km/s (this speed is higher than the speed required to make it orbit in a circle, but less than the escape velocity of the cannonball). If Earth didn't have an atmosphere, what shape does the trajectory of the cannonball have?

The trajectory is an ellipse. The trajectory of any orbiting object is an ellipse

Two trucks of equal mass and equal magnitude of velocity are about to collide head on, predict what will happen.

The trucks will stick together after the collision and not move.

Two trucks are about to collide head on. The green truck has a velocity that is smaller than that of the red truck. What will happen.

The trucks will stick together and move in the direction of the red truck because it has greater velocity.

What is the Newtonian synthesis?

The union of terrestrial laws and cosmic laws.

Predict how the upward force exerted on the feet by the scale will compare to the man's weight if the elevator is moving downward at a constant speed.

The upward force on the feet will be equal to the man's weight.

Predict how the upward force exerted on the feet by the scale will compare to the weight of the man if the elevator is moving upward at a constant speed.

The upward force on the feet will be equal to the man's weight.

Predict how the upward force exerted on the feet by the scale will compare to the man's weight if the elevator is accelerating downward.

The upward force on the feet will be less than the man's weight.

Predict how the upward force exerted on the feet by the scale will compare to the man's weight if the elevator is accelerating upward.

The upward force on the feet will exceed the man's weight.

A baseball is batted at an angle into the air. Once airborne, and ignoring air drag, what is the ball's acceleration vertically? Horizontally?

The vertical acceleration is g (directed downward) because the force of gravity is vertical. The horizontal acceleration is zero because no horizontal force acts on the ball.

A tapered cup rolled on a flat surface makes a circular path. What does this tell you about the tangential speed of the rim of the wide end of the cup compared with that of the rim of the narrow end?

The wide part of the cup rolls faster than the narrow part, because it has greater tangential speed than the narrow end, so it rolls in a curve.

What is true about the work done by a non-conservative force?

The work done by a non-conservative force will always change the total mechanical energy of a system. When the total work done on a system is due to non-conservative forces, that total work done will change the kinetic energy of the system, according to the work-energy theorem: W = ∆KE.

When you lift a book upward off of a table, what is true about the work done on the book by the force of gravity?

The work done by the force of gravity is negative and proportional to the upward displacement of the book. The work done by gravity is negative because the force of gravity, which points downward, is in the opposite direction of the displacement, which is upward. The work done by the force of gravity is proportional to the displacement of the book because the force of gravity is approximately constant everywhere near the surface of Earth.

(7.1) Which requires more work: lifting a 50-kg sack a vertical distance of 2 m or lifting a 25-kg sack a vertical distance of 4 m?

The work done is the same. Since in both cases the force would be the gravitational force of each sack being moved a given distance, the second example shows that even though the sack is moved twice as far it is half as heavy so the two examples would have the same amount of work done.

Consider a problem that asks for the distance of a fast-moving crate sliding across a factory floor and then coming to a stop. What is the most useful equation for solving that problem.

The work energy theorem: Where Fd = ∆½mv²

There is no force as viewed by someone outside the car. To them you move in a straight line.

The graveyard of mechanical energy is what?

Thermal energy.

Consider a batted baseball that follows a parabolic path on a day when the Sun is directly overhead. How does the speed of the ball's shadow across the field compare with the ball's horizontal component of velocity?

They are the same!

You observe two identical balls of putty heading directly toward each other at equal speeds. What can you say about their total kinetic energy?

They have twice the kinetic energy of either ball by itself.

You observe two identical balls of putty headed directly toward each other at the same speed; what can you say about their total momentum?

They have zero total momentum.

If a pipe effectively extends a wrench handle to three times its length, by how much will the torque increase for the same applied force?

Three times more leverage for the same force produces three times more torque. (Caution: This method of increasing torque sometimes results in shearing off the bolt!)

neap tide

Tide that occurs when the Moon is halfway between a new Moon and a full Moon, in either direction. The tides due to the Sun and the Moon partly cancel, so that the high tides are lower than average and the low tides are not as low as average.

From the viewpoint of an observer in the orbiting rocket, what happens to time on the other rocket as it falls toward the event horizon of the black hole?

Time runs increasingly slower as the rocket approaches the black hole.

What does a torque tend to do to an object?

Torques tend to twist or change the rotational motion of things. If you want a stationary object to rotate or a rotating object to change rotational velocity, apply torque.

Momentum of an isolated system

Total momentum is constant. No momentum in or out; momentum can be neither created nor destroyed

Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance?

Twice as much

Who gathered the data that showed planets traveling in elliptical paths around the Sun? Who discovered elliptical orbits? Who explained them?

Tycho Brahe gathered the information. Kepler discovered elliptical orbits. Newton combined everything and explained them.

Inertial frame of reference

Unaccelerated vantage point in which Newton's laws hold exactly

Two cars experience a collision on a city road. Both drivers are using their brakes when the cars hit. Which statement is true?

Using the impulse approximation, conservation of momentum can be applied to the very brief time period of the collision itself (giving approximate results). The collision between the cars involves brief forces that are much stronger than the forces of friction exerted on the cars by the road. Thus if we apply conservation of momentum to a very thin "slice" of time surrounding the collision, the total momentum of the two cars will not change very much and will be approximately conserved.

Single car moving at 10 m/s collides with another car of the same mass, m at rest. What is the final velocity of the system?

V = 5 m/s.

Escape velocity

Velocity that a projectile, a space probe, etc, must reach to escape the gravitational influence of Earth or the celestial body to which it is attracted.

simple harmonic motion

Vibratory or periodic motion, like that of a pendulum, in which the force acting on the vibrating body is proportional to its displacement from its central equilibrium position and acts toward that position.

work-energy theorem formula

W = ∆KE

Precession

Wavering of a spinning object, such that its axis of rotation traces out a cone.

What would the magnitude of the gravitational field be anywhere inside a hollow, spherical planet?

pulley

Wheel that acts as a lever used to change the direction of a force. A pulley or system of pulleys can also multiply forces

(7.1) Cite an example in which a force is exerted on an object without doing work on the object.

When a person pushes on a heavy object, the object doesn't move. The person is exerting a force upon the object but the object does not move distance, therefore, no work is being done.

How do clockwise and counterclockwise torques compare when a system is balanced?

When a system is balanced it is said to be in equilibrium. This means the clockwise and counterclockwise torques are equal and therefore cancel one another out.

When a car drives off a cliff, why does it rotate forward as it falls?

When all the wheels are on the ground, the car's CG is above a support base and no tipping occurs. But when the car drives off a cliff, the front wheels are first to leave the ground and the car is supported only by the rear wheels. The CG then extends beyond the support base, and rotation occurs. Interestingly, the speed of the car is related to how much time the CG is not supported and, hence, the amount the car rotates while it falls.

conservation of angular momentum

When no external torque acts on an object or a system of objects, no change of angular momentum takes place. hence, the angular momentum before an event involving only internal torques is equal to the angular momentum after the event.

According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of the bodies is doubled? If both masses are doubled?

When one mass is doubled, the force between it and the other mass doubles. If both masses double, the force is 4 times as great.

inversely

When two values change in opposite directions, so that if one increases and the other decreased by the same factor, they are said to be inversely proportional to each other.

Why does bending your legs when running enable you to swing your legs to and fro more rapidly?

When you bend your legs you reduce their rotational inertia so that they can rotate back and forth more quickly. Long legged people tend to walk with slower strides than those with short legs. Giraffes, horses, and ostriches run with a slower gait than dachshunds, mice and bugs.

When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?

When you whirl a can in circular motion you apply a force inward. By applying a force in, along the string, you are continually changing the direction of the velocity of the can. This means you provide a centripetal acceleration, which points directly into the center of the can.

center of gravity

Where the object's weight is considered to act

Why does the gravity in the Space Shuttle compare with the gravity on Earth the way it does?

Does the electric power that is generated from wind-powered generators affect the speed of the wind? That is, would locations behind the wind generators be windier if the generators weren't there?

Wind-powered generators subtract KE from the wind, so the wind is slowed by interaction with the blades. So, yes, it would be windier behind the wind generators if they weren't there.

When G was first measured by Henry Cavendish, newspapers of the time hailed his experiment as the "weighing Earth experiment." Why?

With a known mass, a scale, and the radius of Earth, you can calculate the unknown mass of Earth if you know G

Work (W) Formula

Work = force × distance.

work-energy theorem

Work done on an object is equal to the kinetic energy gained by the object. Work = ΔKE

conservation of energy for machines

Work output of any machine at steady state cannot exceed the work input.

Do tides occur in the molten interior of Earth for the same reason that tides occur in the oceans?

Yes due to the difference in gravitational force across the core

Is it correct to say that, if no net impulse is exerted on a system, then no change in the momentum of the system will occur?

Yes, always.

Can an object have energy?

Yes, but in a relative sense. For example, an elevated object may possess PE relative to the ground below but no energy relative to a point at the same elevation. Similarly, the KE that an object has is relative to a frame of reference, usually Earth's surface.

Must a car with momentum have kinetic energy?

Yes, due to motion alone. Any vector or scalar quantities are irrelevant. Any moving object has both momentum and kinetic energy.

Escape speed from Earth is 11.2 km/s. Is it possible to escape from Earth at half this speed? At one-quarter this speed? If so, how?

Yes, escape speed can be less than 11.2 km/s if the speed is sustained long enough.

Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?

Yes. If the car were twice as heavy, its increase in PE would be twice as great.

Ways to express g (gravity)

You can express g in units of N/kg because m/s² is equivalent to N/kg.

Where do you weigh more: at the bottom of Death Valley or atop one of the peaks of the Sierra Nevada? Why?

You weight more in Death Valley because you are closer to the center of the Earth.

A ball is thrown horizontally from a cliff at a speed of 10 m/s . You predict that its speed 1 s later will be slightly greater than 14 m/s . Your friend says it will be 10 m/s.

You, consider the resultant.

When is your weight measured as mg

Your weight is measured as mg when you are strongly supported in a gravitational field of g and in equilibrium.

What is the magnitude of the gravitational field at Earth's center?

Zero.

When a satellite travels at constant speed, the shape of its path is

a circle.

gravitational field

a force field that exists in the space around every mass or group of masses; measured in newtons per kilogram.

abbreviation from center of gravity

If you were inside the rocket that falls toward the event horizon, from your own viewpoint you would __________.

accelerate as you fall and cross the event horizon completely unhindered. From your point of view, time runs normally in your spaceship and gravity must accelerate you as you fall toward the black hole. There is no physical barrier at the event horizon, so you cross it unhindered.

Inside a freely-falling runaway elevator, your

apparent weight is zero

If you were inside the rocket that falls toward the event horizon, you would notice your own clock to be running __________.

at a constant, normal rate as you approach the event horizon. All motion is relative, and you will always consider your own clock to be running at a normal rate

The center of gravity of a basketball is located _______.

at its geometrical center

Where is the center of gravity of the broom that Dr. Hewitt holds up?

at the balance point. The balance point is at the center of the heavier side of the broom.

A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape using a given amount of fuel, should it fire its engines to accelerate forward when it is at the apogee or at the perigee? (Hint: Let the formula Fd=ΔKE be your guide to thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d the rocket would travel during this brief burst at the apogee and at the perigee.)

at the perigee.

gravitation

attraction between objects due to mass.

Why is centrifugal force in a rotating frame called a "fictitious force"?

because it is just the lack of a force to keep an object in rotational motion.

When traveling twice as fast your kinetic energy is increased _______.

by a factor of four

A cannon recoils while firing a cannonball. The speed of the cannon's recoil is relatively small because the

cannon has much more mass than the cannonball.

Centripetal force does no work on a circularly-moving object because

centripetal force has no component in the direction of motion.

When you do somersaults, you'll more easily rotate when your body is

curled into a ball shape

horizontal distance formula

d = vt

Distance for free fall

d = ½gt²

When bullets are fired from an airplane in the forward direction, the momentum of the airplane is

decreased. Newton's third law.

Energy cannot be _______.

destroyed

If the mass of one planet is somehow doubled, the force of gravity between it and a neighboring planet would

double. From F = G(m₁m₂)/ d² If one doubles then the force will double

When the force that produces an impulse acts for twice as much time, the impulse is

doubled. Impulse = force × time. So same force x 2time = an impulse that is twice as great

When the speed of an object is doubled, its momentum

doubles. Because momentum = mass and velocity. If velocity is doubled so is acceleration.

When no air resistance acts on a fast-moving baseball, its acceleration is

downward, g. Without air resistance, acceleration only acts on the vertical component.

Newton's most celebrated synthesis is of

earthly and heavenly laws

A cannon fires a cannonball horizontally. Right after the cannonball is fired, the magnitude of the momentum of the cannonball is ________ that of the cannon. Ignore friction between the cannon and the ground.

equal to. Due to conservation of momentum, the momentum of the cannon must be equal and opposite than of the fired cannonball.

The impulse approximation is used in situations where __________.

external forces on the system are present, but they are small compared to the large, brief internal forces between parts of the system

Momentum is conserved in the absence of

external forces. Internal systems that have no outside forces have no change in momentum.

A boxer rides with the punch so as to reduce _______.

force

The torque exerted by a crowbar on an object increases with increased _______.

force and leverage distance

The work that is done when twice the load is lifted twice the distance is _______.

four times as much.

The tangential speed on the outer edge of a rotating carousel is _______.

greater than toward the center

When an elevator accelerates upward, your weight reading on a scale is

greater. The support force pressing on you is greater.

Consider a planet with an elliptical orbit around the Sun. Its average distance from the Sun is __________.

half the distance along a line from the nearest to the farthest points in its orbit. The line that passes through the Sun and connects the nearest and farthest points in the orbit is called the major axis, and half this line is the semimajor axis — which is the planet's average distance from the Sun.

Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of car A, the speed of the coupled freight cars is

half. After the collision, the mass of the moving freight car has doubled. Twice the mass = half the velocity.

A block of ice sliding down an incline has half its maximum kinetic energy

halfway down

Cassy can get more force on the bricks she breaks with a blow of her bare hand when _______.

her hand is made to bounce from the bricks.

A person weighs 150 pounds. He is standing on a scale inside an elevator. The elevator is moving downward and slowing down (coming to a stop). What is the reading of the scale?

higher than 150 pounds Since the elevator is slowing down while moving downwards, the person is accelerating upwards. This means that the normal force must be greater than the magnitude of the force of gravity.

A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater: average force. impulse. both. none

impulse. The average force on the cannonball will be the same for a short or long barreled cannon. The longer barrel provides a longer time for the force to act and therefore a greater impulse.

According to Kepler, the line from the Sun to any planet sweeps out equal areas of space

in equal time intervals. Kepler's second law.

Where is the center of gravity of a donut?

in the hole

What are the two ways to increase impulse?

increase the force or increase the time the force is applied

When the distance between two stars decreases by one-third, the force between them

increase to nine times as much. From Newton's Law of Gravity.

A 150 pound astronaut is inside the space shuttle, orbiting around the Earth just above the Earth's atmosphere (the atmosphere's thickness is very small compared to the radius of the Earth). The force of gravity acting on the astronaut

is roughly 150 pounds. Even though the astronaut is in a state of free fall and feels weightless, the force of gravity is still the same as if he were standing on Earth's surface.

How does the force needed to turn the wrench change if you increase the lever arm?

it decreases

A pendulum is swinging back and forth. When it is in its lowest position (oriented straight down),

its kinetic energy is higher than when the pendulum is making a U turn. It is moving the fastest at this position, so its kinetic energy is largest here.

A person throws a ball straight upwards. When the ball is at its highest point above the ground, what happens to its total energy?

its total energy is the same as right after the ball was thrown. Its kinetic energy is zero, but it now has potential energy. Energy is conserved, and here all the energy is in the form of potential energy.

GPE units

joules.

The units for momentum are

kg * m/s

Kinetic energy units

kg * m²/s² or Joule (J)

angular momentum units

kgm²/s

When an elevator accelerates downward, your weight reading is

less. The support force is less.

If you can't avoid being hit by a fast-moving object, you'll suffer a smaller contact force if you can extend that force over a

longer time.

Torque units

m × N

The constant G in Newton's equation _______.

makes the units of measurement consistent

centripetal force equation

mass * tangential speed² / radius.

centripetal force depends on

mass of object, tangential speed of the object and the radius of the circle. Therefore: mass * tangential speed² / radius.

An object is lifted from the surface of a spherical planet to an altitude equal to the radius of the planet. As a result, which of the following changes in the properties of the object take place?

mass remains the same; weight decreases

momentum forumla

mass x velocity

The force of gravity between two planets depends on their

masses and distances apart. The equation for gravitational force cites only masses and distances as variables.

When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it makes

matches the curved surface of Earth. For an 8 km tangent, Earth curves downward 5m. Therefore a projectile traveling horizontally at 8 km/s will fall 5 m in that time and follow the curve of the Earth.

megajoules, a million joules.

To calculate the gravitational force between two objects we __________, and then multiply by the gravitational constant

multiply the two masses, divide by their distance squared

Work units

newton meter (Nm) or Joule (J)

The momentum of a system is conserved during a certain process only if __________.

no net external force is exerted on the system during that process

If you push against a stationary brick wall for several minutes, you do no work

on the wall. Work is force * distance. The wall does not move therefore no work is done.

Suppose you stepped into a hole bored clear through the center of Earth and made no attempt to grab the edges at either end. Neglecting air drag, what kind of motion would you experience?

ou would oscillate back and forth. If Earth were an ideal sphere of uniform density and there were no air drag, your oscillation would be what is called simple harmonic motion. Each round-trip would take nearly 90 minutes. We will see in Chapter 10 that an Earth satellite in close orbit about Earth also takes 90 minutes to make a complete round-trip. (This is no coincidence: If you study physics further, you'll learn that "backand- forth" simple harmonic motion is simply the vertical component of uniform circular motion—interesting stuff.)

turbine

paddle wheel driven by steam, water, etc that is used to do work

fulcrum

pivot point of a lever

power formula

power = work / time interval. also ∆energy/time interval

A job can be done slowly quickly. Both may require the same amount of work, but different amounts of what?

power. Power is the rate at which work is done.

Kepler's third law states that for any planet orbiting the Sun, the orbital period squared is equal to the average orbital distance cubed. This implies that __________.

p² = a³. This implies a planet with a large average distance from the Sun has a longer orbital period than a planet with a smaller average distance from the Sun.

The work done in bringing a moving car to a stop is the force of tire friction x stopping distance. If the initial speed of the car is doubled, the stopping distance is

quadruple the distance. Twice the speed means four time the kinetic energy and four times the stopping distance.

If the masses of two planets are somehow doubled, the force of gravity____

quadruples

If the masses of two planets are each somehow doubled, the force of gravity between them

quadruples. From F = G(m₁m₂)/ d² If both masses are doubled then the force would four times greater.

If Quantity X is conserved for a certain system and during a certain process, that means__________.

quantity X for that system does not change in any way during that process. A conserved quantity's total value for a system does not change at all

Tangential Speed Formula

radial distance * rotational speed symbolized as: rω

The velocity of a typical projectile can be represented by horizontal and vertical components. Assuming negligible air resistance, the horizontal component along the path of the projectile

remains the same. Without air resistance there is nothing to increase or decrease the horizontal component.

rotational speed units

revolutions / min. rev/seconds. degree/min. radian/sec.

angular momentum formula

rotational inertia * angular velocity

Suppose a rocket ship, while sitting on Earth, has a weight of 10,000 N. The rocket ship takes off and reaches a distance from Earth's center of 3REarth. What is the force due to gravity acting on the spaceship?

roughly 1,100 N The force of gravity here is 1/9th that when on the surface.

A person weighs 150 pounds. He is standing on a scale in an elevator and stands on a scale. The elevator is accelerating upwards at a rate of 10 m/s/s, what is the reading of the scale?

roughly 300 pounds The upward force of the scale minus the force of gravity is equal to the mass times acceleration. Since the acceleration is roughly g (9.8 m/s/s), this means that the upward force needs be 2mg.

A cannonball is fired horizontally from the top of the highest mountain on Earth. If Earth didn't have an atmosphere, what initial speed is required such that the cannonball orbits around the Earth in a circle?

roughly 8 km/s. With this speed, it would take about 85 minutes to go around the Earth!

A bicycle that travels four times as fast as another when braking to a stop will skid

sixteen times as far.

As the falling rocket plunges toward the event horizon, an observer in the orbiting rocket would see that the falling rocket __________.

slows down as it approaches the event horizon, and never actually crosses the event horizon

How does speed affect the friction between a road and a skidding tire?

speed does not affect friction; friction affects force.

Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.

the Moon has a larger acceleration than Earth, because it has a smaller mass. Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.

A record player is spinning with a certain rotational speed. One ant is standing half way between the center of the record and the edge, and another ant is standing on the edge. Which ant is moving faster?

the ant on the edge. Since the ant on the edge travels around a bigger circle in the same amount of time as the other ant, it is moving faster.

The moment of inertia of a rotating ice skater is largest when

the arms are held perpendicular to her body

If you are standing on a scale in an elevator, what exactly does the scale measure?

the force exerted on the scale

No work is done by gravity on a bowling ball that rolls along a bowling alley because

the force on the ball is at right angles to the ball's motion.

Tangential speed

the linear speed tangent to a curved path, such as in circular motion

rotational inertia

the resistance of an object to changes in its rotational motion. Depends on the mass of an object and the distribution of mass around axis of rotation. (Second Law; a=Fnet/mass) The greater the distance between an object's mass concentration and the axis, the greater the rotational inertia.

An object is dropped and freely falls to the ground with acceleration g. If it is thrown upward at an angle instead, neglecting air drag, its acceleration will be

the same. g will always be 9.8 m/s

Without air drag the speed lost while going up equals____

the speed gained while coming down. Time going up, equals time coming down.

How does Earth's curvature relate to the speed needed for a projectile to orbit Earth?

the speed must be great enough so that the path of the projectile follows earth's curvature, instead of falling into it.

gravitational potential energy is also equal to_____

the work done, which is the force required to move an object upward × the vertical distance moved against gravity.

You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is

twice as much.

If you place a pipe over the end of a wrench when trying to rotate a stubborn bolt, effectively making the wrench handle twice as long, you'll multiply the torque by

two.

To impart the greatest momentum to an object, should you exert the largest force possible, extend that force for as long a time as possible, or both? Explain.

use the largest force for as long a time as possible Ft=mV

speed formula

v = d/t

Speed of a satellite in circular orbit formula

v = √gravity × mass / distance. G is the universal gravitational constant, M is the mass of Earth (or whatever body the satellite orbits), and d is the distance of the satellite from the center of Earth or other parent body.

The speed of a satellite in an elliptical orbit

varies. A satellite in an elliptical orbit cycles between receding from Earth and losing speed and approaching Earth and gaining speed.

power units

watts. 1 joule/second = 1 watt.

When the elevator cable breaks, the elevator falls freely so your weight reading is

zero. There is zero support force on you.

If a trapeze artist rotates once each second while sailing through the air and contracts to reduce her rotational inertia to one-third of what it was, how many rotations per second will result?

ω= 3 rotations per second.

Suppose a ball of putty moving horizontally with 1 kg·m/s of momentum collides with and sticks to an identical ball of putty moving vertically with 1 kg·m/s of momentum. What is the magnitude of their combined momentum?

1.41 kg·m/s

A green truck is moving to the right. A red truck is moving to the left with a speed of 6 m/s. The mass of the red truck is 1,000 kg and the mass of the green truck is 3,000 kg. How fast must the green truck be moving such that ,if it collides head-on with the red truck and the two trucks stick together, the final velocity of the two trucks is zero?

2 m/s. Since the green truck is three times more massive, it needs a speed 1/3 that of the red truck in order for its momentum to be equal and opposite that of the red truck.

A green truck is moving to the right with an initial speed of 9 m/s. It collides head-on with a yellow truck, initially at rest. After the collision, the two trucks are stuck together. The green truck is twice as massive as the yellow truck. Immediately after the collision, what is the speed of the two trucks?

6 m/s. Since the final mass of the two trucks is three halves the mass of the green truck, the final speed of the two trucks needs to be two thirds of the initial speed of the green truck

A green truck is moving to the right with a speed of 10 m/s. A red truck is moving to the right with a speed of 2 m/s. The mass of the two trucks are equal. If the two trucks have an inelastic collision, what is the speed of the two trucks right after the collision?

6 m/s. The velocities don't add together. If they did, the total momentum would be much larger than the initial momentum of the system. Since momentum is conserved and the masses of the trucks are the same, the final velocity is equal to the average of the two velocities.

How much impulse stops a 60-kg carton sliding at 4.0 m/s when it meets a rough surface?

60 kg × 4 m/s = J = 240 N × s. The question is looking for the force of friction the carton receives upon meeting the rough surface.

In which of these processes is the momentum of the object conserved? An asteroid (the object) accelerates steadily toward the moon. A car (the object) pulls away from a stop sign. A cyclist (the object) collides with a pedestrian. A train (the object) goes around a curve at a steady speed. A skydiver (the object) with her parachute deployed falls toward the ground at a steady speed.

A skydiver (the object) with her parachute deployed falls toward the ground at a steady speed. Having a quantity be conserved means that it doesn't change. In order for momentum to be conserved it must have an unchanging mass and velocity (including both speed and direction).

Which has more momentum: a 1-ton car moving at 100 km/h or a 2-ton truck moving at 50 km/h?

Both have the same momentum (1 ton × 100 km/h = 2 ton × 50 km/h).

elastic collision

Collision in which colliding objects rebound without lasting deformation or heat generation.

inelastic collision

Collision in which the colliding objects become distorted and/or generate heat during the collision and possible stick together.

Two hockey players collide on the ice. Which statement reflects how we can apply conservation of momentum to this situation?

During the very brief collision the total momentum of the two players (the system) is a conserved quantity. The momentum of each player is not itself a conserved quantity since they both experience a net force during the collision. It is the total momentum of the system (the two players, in this case) that can be considered to be conserved since the system experiences no net external force. However, we can only consider it to be conserved if we restrict ourselves to just the brief collision between the players. If we extend our time to include time before and after the collision, the players might use their skates to change speed or direction (using external forces) and the total momentum of the two skaters would no longer be conserved.

How is the impulse-momentum relationship related to Newton's second law?

F net=ma ma=mΔv/Δt so Ft=Δmv

True or False: The momentum of a big, massive truck is always greater than the momentum of a person riding a bicycle.

False. Since momentum is mass times velocity, the truck could have very little momentum if it is moving very, very slowly.

Distinguish between force and impulse.

Force is a push or pull. An impulse is the product of the force acting on an object and the time during which it acts.

An ostrich egg of mass m is tossed at a speed v into a sagging bed sheet and is brought to rest in a time t. Find the force acting on the egg when it hits the sheet.

From Ft = mv. F = mv/t

When does impulse equal momentum?

Generally, impulse equals a change in momentum. If the initial momentum of an object is zero when the impulse is applied, final momentum = impulse applied. And, if an object is brought to rest, initial momentum = impulse delivered.

Imagine that you replace the block in the video with a happy or sad ball identical to the one used as a pendulum, so that the sad ball strikes a sad ball and the happy ball strikes a happy ball. The target balls are free to move, and all the balls have the same mass. In the collision between the sad balls, how much of the balls' kinetic energy is dissipated?

Half of it. The collision between the sad balls is completely inelastic, and due to the conservation of momentum, the velocity of the balls after the collision will be half the velocity of the incoming ball before the collision. The expression for kinetic energy is ½mv², and while there is double the mass moving after the collision as before, the decrease in velocity by a factor of two results in the overall kinetic energy being half its initial value.

How does Dr. Hewitt break the piece of wood?

He causes a change in momentum of his hand over a short period of time.

relationship of impulse and momentum

Impulse is equal to the change in the momentum of the object that impulse acts upon. In symbol notion, Ft = ∆mv

Cassy breaks a stack of bricks with her hand. How does the force that Cassy exerts on the bricks compare with the force exerted on her hand?

In accord with Newton's third law, the forces are equal. Only the resilience of the human hand and the training she has undergone to toughen her hand allow this feat to be performed without broken bones.

Conservation of momentum

In the absence of a net external force, the momentum of ab object or system of objects is unchanged. mv (before event) = mv(after event)

law of conservation of momentum

In the absence of an external force, the momentum of a system remains unchanged. Hence, the momentum before an event involving only internal forces is equal to the momentum after the event. mass × velocity (before event) = mass × velocity (after event)

momentum

Inertia in motion. The product of the mass and the velocity of an object (provided the speed is much less than the speed of light). Has magnitude and direction and therefore is a vector quantity. Also called linear momentum, and abbreviated p. p = mv

What does it mean to say that momentum (or any quantity) is conserved?

It means that momentum doesn't change. Momentum before an event = momentum after an event.

When you are struck by a moving object, is it favorable that the object makes contact with you over a short time or over a long time? Explain.

Long contact time decreases the magnitude of the average force and is favorable.

Can you produce a net impulse on an automobile if you sit inside and push on the dashboard? Can the internal forces within a soccer ball produce an impulse on the soccer ball that will change its momentum?

No impulses must be exerted from outside of the system. Internal impulses do not cause momentum.

When a cannonball is fired, momentum is conserved for the system cannon + cannonball. Would momentum be conserved for the system if momentum were not a vector quantity? Explain.

No. If velocity was not a vector quantity, then it would always have a positive value. So when the cannon and the cannonball went in opposite directions, their momentums would not cancel each other out, but would instead double the overall momentum of the system.

During a complex collision between many objects, including object A and object C, the impulse exerted on object A by object C is equal to __________. the impulse exerted on object C by object A None of the listed responses is correct. the change in the momentum of object A the change in the momentum of object C

None of these are correct. Impulse is a vector quantity. Because of Newton's third Law the two objects must exert equal and opposite forces on each other. Since they will do so for equal amounts of time they will exert impulses with equal magnitudes but opposite directions on each other. The change in momentum of an object equals the net impulse exerted on it during the collision, which is not the same as any single impulse it experiences.

Impulse units

N×s

cyclotron

Particle accelerator that imparts high energy to charged particles such as protons, deuterons, and helium ions.

neutron star

Star that has undergone a gravitational collapse in which electrons are compressed into protons to form neutrons.

For the same force, which cannon imparts a greater impulse to a cannonball: a long cannon or a short one?

The long cannon imparts a greater impulse because the force acts over a longer time. (A greater impulse produces a greater change in momentum, so a long cannon imparts more speed to a cannonball than a short cannon.)

Suppose a gliding cart of mass .5kg bumps into and sticks to a stationary cart of a mass 1.5 kg. If the speed of the gliding cart before the collision is Vbefore, how fast will the coupled carts glide after the collision.

The momemtum of the .5kg cart will = the momentum of the carts stuck together. So .5kg × V₁ = (.5kg + 1.5kg) × V₂. You're searching for V₂, so therfore: V₂ = .5kg × .5kg × V₁ / 2kg. = .25 × V₁. Therefore the new speed is only ¼ of the original speed. This makes sense because the new mass is also 4 times as large.

Playing in the rain, a little girl tackles a little boy. Just before she tackles him, the boy is running east at 3 m/s and the girl is running south at 4 m/s. After the tackle, the girl holds on and the two slide on the wet grass. Our system consists of just the two children. Immediately after the tackle, what can we say about how the momenta of each child compare?

The momentum of both children will be in the same direction. Because the girl holds on after the tackle the two children will be moving in the same direction at the same speed. Thus we know they will each have momentum in the same direction. Unless the two children happen to have exactly the same mass, they will not have equal momenta. Since the system had a non-zero momentum just before the collision, the system cannot have zero momentum after the collision. That would violate the conservation of momentum.

Two asteroids are flying through space, each with an unknown momentum, p1 and p2. Which of these is a true statement about the x-component of their total momentum, p sub x?

The momentum of the x component must have a magnitude between zero and the sum of the magnitudes of their individual momenta. Meaning 0 ≤ |p of x | ≤ (|p₁| + |p₂|).

A boxer being hit with a punch contrives to extend time for best results, whereas a karate expert delivers a force in a short time for best results. Isn't there a contradiction here?

There is no contradiction because the best results for each are quite different. The best result for the boxer is reduced force, which is achieved by maximizing time, and the best result for the karate expert is increased force delivered in minimum time.

Newton's second law states that, if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs?

Yes, because no acceleration means that no change occurs in velocity or in momentum (mass × velocity). Another line of reasoning is simply that no net force means there is no net impulse and thus no change in momentum.

Newton's third law states that the force a cannon exerts on a cannonball is equal and opposite to the force the cannonball exerts on the cannon. Does it follow that the impulse the cannon exerts on the cannonball is equal and opposite to the impulse the cannonball exerts on the cannon?

Yes, because the interaction between both occurs during the same time interval. Since the times are equal and the forces are equal and opposite, the impulses Ft are also equal and opposite. Impulse is a vector quantity and can be canceled.

Does a moving object have momentum?

Yes, but, like velocity, in a relative sense—that is, with respect to a frame of reference, usually Earth's surface. The momentum possessed by a moving object with respect to a stationary point on Earth may be quite different from the momentum it possesses with respect to another moving object.

A fast moving car hitting a haystack or hitting a cement wall produces different results? Do they both experience the same change in momentum? The same impulse? The same force?

Yes, they experience the same change in momentum and impulse. Although stopping the momentum is the same whether done slowly or quickly, the force on impact is vastly different.

If some quantity, let's call it "Z," is conserved for a certain system, during a certain process, that means __________.

Z for that system does not change in any way during that process. This also must mean that any change in Z for parts of the system during the process is offset by an equal but opposite change for the Z of other parts of the system.

Momentum __________.

is a vector, with a magnitude and a direction

A slowly moving ship can have a greater momentum than a fast-moving racing car when _______.

its mass times velocity is greater than that of the car.

Momentum units are

kg × m/s

momentum formula

mass × velocity

If two cars have the same mass and speed they __________.

might have the same momentum but might not because direction is not specified.

If the equally massive cars of the preceding question stick together after colliding inelastically, how does their speed after the collision compare with the initial speed of car A?

momentum = mass x velocity. After collison, the two cars become one unit and stick together. Since mass is doubled, velocity is only at ½.

An orange car is moving eastward with a speed of 10 m/s. A purple car is moving northward with the same speed. The two cars undergo an inelastic collision. The orange car has a mass of 3000 kg and the purple car has a mass of 1000 kg. After the collision, the two cars?

move off in a direction nearly eastward, but they also have a small northward component (east, northeast). Since the magnitude of momentum in the east direction is three times greater than that in the north direction, the final velocity needs a higher component in the eastward direction.

What is the momentum of an 8.8-kg bowling ball rolling at 1.8 m/s ? Round to two significant figures.

p = 16 kg×m / s

What impulse occurs when an average force of 10 N is exerted on a cart for 2.5 s ?

p = 25 kg ×m / s

The quantity that is called impulse can be measured by the _______.

product of force and time.

When a big fish swims into an oncoming smaller fish and swallows it, the momentum of the two-fish system _______.

remains the same.

An orange car is moving eastward with a speed of 10 m/s. A purple car is moving northward with the same speed. The two cars undergo an inelastic collision. If the cars have the same mass, how fast are the two cars moving (together) after the collision?

roughly 7 m/s. The momentum is conserved in each direction, so the final speed in the northward direction is 5 m/s (since the combined mass is twice as high as either car) and the final speed in the eastward direction is 5 m/s. So the final speed is equal to the hypotenuse of a triangle with the two other sides being 5 m/s.

A green ball is moving to the right with an initial speed of 5 m/s. It collides head-on with a yellow ball, initially at rest. Both balls have the same mass. After the collision,

the green ball is stationary and the yellow ball moves to the right with a speed of 5 m/s. Both momentum and energy is conserved.

The change in an object's momentum during a certain time interval is equal to __________.

the net force exerted on the object times the duration of the time interval

During a large, multi-object collision that involves object C, the change in the momentum of object C is equal to __________.

the net impulse exerted on object C The impulse momentum theorem says that any change in an object's momentum always occurs due to a net impulse exerted on that object.

Which has a greater momentum: a heavy truck at rest or a moving skateboard?

the skateboard

Ball 1 has a mass of 2m and speed v, while ball 2 has mass m and speed 2v. Both balls are moving at 45º angles with respect to the vertical. Our system consists of just the two balls and is isolated from external forces. Just before the collision __________.

the total horizontal component of the momentum of the system is zero. The magnitude of each ball's momentum is the same and since they have symmetric angles relative to the vertical direction, they will both have the same magnitude x-component, given by |p sub x| = p x cosine of 45°. Since their horizontal components of momentum are oppositely directed, they will cancel out and the total horizontal component of the momentum of the system is zero.

Two balls are about have a head-on collision. Ball A has a mass m and speed of 2v, whereas ball B has mass 2m and speed v. Our system consists of just the two balls and is isolated from external forces. Just after the collision ______.

the total momentum of the system must be zero. Because of their initial masses, speeds, and directions, the two balls end up having initial momenta that have equal magnitudes but opposite directions. Thus the total momentum of the system before the collision is zero.

Physics Chapter 6 Momentum, Chapter 7 Energy, Physics Chapter 8 Rotational Motion, Chapter 10 Projectile Motion Physics, Chapter 9 Physics Gravity

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