Homework Questions
What is the net force on an apple that weighs 1 N when you hold it at rest above your head? What is the net force on it after you release it?
0 N. 1 N.
Two automobiles, each of mass 1300 kg, are moving at the same speed, 18 m/s, when they have an inelastic collision. (a) In what direction and at what speed does the wreckage move if one car was driving north and one south? (b) In what direction and at what speed does the wreckage move if one car was driving north and one east (as shown in the figure)?
0 m/s (no direction). 25.45 m/s^2 45 degrees NE.
The value of g at the Earth's surface is about 9.8 m/s2. What is the value of g at a distance of four times the Earth's radius?
0.613 m/s^2
Students in lab measure the speed of a steel ball launched horizontally from a table top to be 3.0 m/s. If the table top is 1.7 m above the floor, where should they place a 20 cm tall tin coffee can to catch the ball when it lands?
1.659 m.
What is the acceleration of a rock at the top of its trajectory when thrown straight upward? (Is your answer consistent with Newton's second law?)
10 m/s^2 in the downward direction.
On a slide a child has a potential energy that decreases by 1000 J while her kinetic energy increases by 900 J. What other form of energy is involved and how much?
100 J is lost to forms of energy such as heat and sound.
Two 100 N weights are attached to a spring scale as shown. Does the scale read 0, 100, or 200 N, or give some other reading? (Hint: Would it read any differently if one of the ropes were tied to the wall instead of to the hanging 100 N weight?) Explain.
100 N. The scale is just measuring the one weight hanging from the bottom of it. The other weight is essentially there to keep the system stationary. The scale would read no differently if the other rope was tied to the wall.
A 4.5 kg fish swimming 3 m/s swallows an absent minded 1 kg fish swimming toward it at a velocity that brings both fish to a halt immediately after lunch. What is the velocity v of the smaller fish before lunch?
13.5 m/s
Find the change in the force of gravity between two planets when the distance between them is decreased by four.
16 times greater
A boxer punches a sheet of paper in mid air, and brings it from rest up to a speed of 27 m/s in 0.05 s. If the mass of the paper is 0.004 kg, what force does the boxer exert on it?
2.16 N
To tighten a bolt, you push with a force of 60 N at the end of a wrench handle that is 0.35 m from the axis of the bolt. What torque are you exerting? If you move your hand inward to be only 0.05 m from the bolt, what force do you have to exert to achieve the same torque? Do your answers depend on the direction of your push relative to the direction of the wrench handle? (Why or why not?
21 Nm 420 N Yes, torque depends on three factors: the magnitude of the force, the direction in which the force acts, and the point at which it is applied to an object. If you change the direction of the push, you are changing the direction in which the force acts, and therefore the answers would be different.
A car crashes into a wall at 35 m/s and is brought to rest in 0.1 s. Calculate the average force exerted on a 75 kg test dummy by the seat belt.
26250 N.
Gravity on the moon is only 1/6 as strong as gravity on the Earth. What is the weight of a 18 kg object on the moon and on the Earth? What is its mass on the moon and on the Earth?
28.8 N (moon), 180 N (Earth) 18 kg (moon), 18 kg (Earth)
If you stand next to a wall on a frictionless skateboard and push the wall with a force of 36 N, how hard does the wall push on you? If your mass is 54 kg, what's your acceleration?
36 N. 0.66 m/s^2
If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was, how many rotations per second will result?
4 rev/s
What is the acceleration of a 35 kg block of cement when pulled sideways with a net force of 170 N?
4.857 m/s^2
An airplane is flying horizontally with speed 1000 km/h (280 m/s) when an engine falls off. (a) Neglecting air resistance, if it takes 32 s for the engine to hit the ground how high is the airplane? (b) If it takes 32 s for the engine to fall how far horizontally does the engine travel while it falls? (c) If the airplane somehow continues to fly as if nothing had happened, where is the engine relative to the airplane at the moment the engine hits the ground?
5.0176 km. 8960 m. Directly below the plane.
Upon which will air resistance be greater; a sheet of falling paper or the same paper wadded into a ball that falls at a faster terminal speed?
A falling sheet of paper experiences a greater air resistance because the unwadded paper has more surface area to be impacted by air resistance than does the wadded one.
At what point in its motion is the KE of a pendulum bob a maximum? At what point is its PE a maximum? When its KE is half its maximum value, how much PE does it have?
ASK ABOUT THIS
Most people today know that the ocean tides are caused principally by the gravitational influence of the moon. And most people, therefore, think that the gravitational pull of the moon on the Earth is greater than the gravitational pull of the sun on the Earth. What do you think?
ASK ABOUT THIS
Consider a baseball player batting a ball. Identify the action-reaction pairs when the ball is being hit. Identify the action-reaction pairs when the ball is in flight.
Being hit: Action: The bat exerts a force on the ball. Reaction: The ball exerts a force on the bat. Flight: Action; Earth pulls down on ball (weight). Reaction; ball pulls up on Earth. And, action; air pushes ball and reaction; ball pushes air.
If you could somehow tunnel inside a star, would your weight increase or decrease? If, instead, you somehow stood on the surface of a shrinking star, would your weight increase or decrease? Why are the answers different?
Decrease. Increase. If the star is shrinking, your weight would increase because the gravitational pull increases as you reach the center of the star. If you tunnel into the star, however, the shell outside of you cancels an increasing portion of the gravitational force so you would weigh less.
The occupant inside a future rotating space habitat feels that she is being pulled by artificial gravity against the outer wall of the habitat (which becomes the "floor"). Explain what is going on in terms of Newton's laws and centripetal force.
If the floor were not present, she would want to continue to move tangent and fly off of the habitat, as stated by Newton's first law. However, at the correct speed, the floor that is stopping her simulates the feeling of gravity as it keeps her in the habitat. The force acting on her and the habitat, however, is still center-seeking.
If the Earth somehow expanded to a larger radius, with no change in mass, how would your weight be affected? How would it be affected if the Earth instead shrunk? (Hint: Let the equation for gravitational force guide your thinking.)
If the radius increases but the mass does not, the distance between the two objects increases, and therefore your weight would decrease. If the radius decreases, the distance between the two objects decreases and your weight would increase.
When the space shuttle coasts in a circular orbit at constant speed about the Earth, is it accelerating? If so, in what direction? If not, why not?
It is accelerating because it changes direction constantly as it orbits the Earth. The acceleration is towards the center of the Earth.
In terms of impulse and momentum, why do airbags in cars reduce the chances of injury in accidents?
Momentum and impulse remain the same regardless of whether a car crashes with or without airbags. However, airbags extend the time in which momentum is reduced, meaning a smaller force is exerted over a longer time, which reduces the chances of injury.
Somewhere between the Earth and the moon, gravity from these two bodies on a space pod would cancel. Is this location nearer the Earth or the moon?
Nearer the moon
Explain how the conservation of momentum is a consequence of Newton's third law.
Newton's third law says that for every action there is an equal and opposite reaction. Since force is proportional to change in momentum, a change in momentum also has to be balanced by an equal and opposite change in momentum. So the conservation of momentum is a consequence of Newton's third law.
Consider: If you throw a ball horizontally while standing on roller skates, you roll backward with a momentum that matches that of the ball. Yet if you go through the motions of throwing but hold on to the ball, you will not roll backward. This can be explained in terms of momentum conservation and in terms of Newton's third law. Explain in terms of Newton's third law.
Newton's third law states that for every action there is an equal and opposite reaction. In the case of not releasing the ball, there is no action/reaction pair. Once the ball is released, the action of throwing it causes a reaction that sends the thrower in the opposite direction with the equal amount of force.
Free fall is motion in which gravity is the only force acting. Is a sky diver who has reached terminal speed in free fall? Explain.
No. Terminal speed is the point at which an object ceases to accelerate due to resistance, therefore air resistance is a force to be considered in the system and the force of gravity is not the only force acting on the object.
Is the force of gravity stronger on a piece of iron than a piece of wood if both have the same mass? Defend.
No. The material of the object does not matter, just their mass. If mass is the same the force of gravity will be the same.
Why does the force of gravity do work on a car that rolls down a hill, but no work when it rolls along a level part of the road?
On a flat surface, the force of gravity on the car is completely counteracted by the normal force. On a hill, only part of the force of gravity is counteracted by the normal force, therefore it accelerates.
If a golf ball and a Ping Pong ball move with the same kinetic energy, can you say which has the greater speed? Explain in terms of the definition of KE. Similarly, in a gaseous mixture of massive molecules and light molecules with the same average KE, can you say which have the greater speed?
Since they have the same kinetic energy, and the masses are different, the ping pong ball must move faster. KE depends on mass and velocity, more of its KE is made up of mass, so it doesn't move as fast. For the same reason, the lighter molecules would move more quickly also.
In the absence of air resistance, if a ball is thrown vertically upward with a certain initial speed, on returning to its original level it will have the same speed. When air resistance is a factor, will the ball be moving faster, the same, or slower than its throwing speed when it gets back to the same level? Why? (Physicists often use a "principle of exaggeration" to help them analyze a problem. Consider the exaggerated case of a feather, not a ball, because the effect of air resistance on the feather is more pronounced and therefore easier to visualize.
Slower. Air resistance acts in a direction opposite to the motion and slows it down.
Does the KE of a car change more when it goes from 10 to 20 km/h or when it goes from 20 to 30 km/h?
The KE changes more from 20 to 30 km/h.
Which will have the greater acceleration rolling down an incline - a bowling ball or a volleyball? Defend.
The bowling ball wins. The bowling ball has less rotational inertia per unit of mass.
Strictly speaking, as more and more skyscrapers are built on the surface of the Earth, does the day tend to become longer or shorter? And strictly speaking, does the falling of autumn leaves tend to lengthen or shorten the 24-hour day? What physical principle supports your answers?
The day tends to become longer. Falling leaves shorten the 24-hour day. The closer the mass is to the center of the Earth, the more quickly it spins, the further away from the center of the Earth the more slowly it spins.
A crate remains at rest on a factory floor while you push on it with a horizontal force F. How big is the friction force exerted on the crate by the floor? Explain.
The force of friction is equal and opposite to the horizontal force F acting on the crate because the crate remains at rest.
If a Mack truck and Honda Civic have a head-on collision, upon which vehicle is the impact force greater? Which vehicle experiences the greater acceleration? Explain.
The force on both vehicles is the same. The acceleration of the Honda Civic is greater. For every action, there is an equal and opposite reaction. Both vehicles exert the same amount of force on each other. Their different masses cause them to accelerate differently.
In the absence of air drag, why does the horizontal component of a projectile's motion not change, while the vertical component does?
The horizontal component cannot change unless there is another force acting on it. If there is no air drag, the only force acting on the object is the force of gravity.
Light consists of tiny "corpuscles" called photons that possess momentum. This can be demonstrated with a radiometer, shown in the sketch. Metal vanes painted black on one side and white on the other are free to rotate about the point of a needle mounted in a vacuum. When photons are incident on the black surface, they are absorbed; when photons are incident upon the white surface, they are reflected. Upon which surface is the impulse of incident light greater, and which way will the vanes rotate? (They rotate in the opposite direction in more common radiometers where air is present in the glass chamber; your instructor may tell you why.) Explain.
The impulse is greater on the silvered side, so the vanes rotate clockwise as viewed from above. ASK ABOUT THIS
If the polar ice caps of the Earth were to melt, the oceans would be deeper by about 30 m. What effect would this have on the Earth's rotation?
The mass contained in the ice would spread more evenly around the world instead of being localized near the poles. According to the conservation of angular momentum, since mass is moving farther from the axis of rotation, the rotational speed decreases. So Earth would slow in its daily rotation and the day would become longer.
Since the moon is gravitationally attracted to the Earth, why doesn't it simply crash into the Earth?
The moon's tangential velocity is what keeps the moon orbiting the Earth.
Why must you bend forward when carrying a heavy load on your back?
To distribute your mass so the center of gravity is above your support base.
You sit at the middle of a large turntable at an amusement park as it is set spinning and then allowed to spin freely. When you crawl toward the edge of the turntable, does the rate of the rotation increase, decrease, or remain unchanged? What physics principle supports your answer?
The rate of rotation decreases. The rate of rotation decreases as the mass moves further away from the center of the turntable, meaning rotational inertia increases. Angular momentum is the product of rotational inertia and the rate of rotation. There is no external torque acting on the system, therefore for angular momentum to remain the same, the rate of rotation must decrease.
An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels, such as those of snow tires, are used, will the speedometer reading be high or low - or no different?
The speedometer will read too low.
A long track balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. Does the track tip clockwise, tip counterclockwise, or remain in balance as the balls roll outward? What principles do you use for your explanation?
The track will remain in equilibrium. The center of mass is initially located directly above the pivot. When the two balls spring apart from each other, they do so in a manner that leaves the center of mass the same. So after they spring apart, the center of mass still remains directly above the pivot so the track remains in balance.
Why is it easier to carry the same amount of water in two buckets, one in each hand, than in a single bucket?
The water in two buckets does not change your center of gravity, but the water in one bucket will.
How does the weight of a falling body compare with the air resistance it encounters after it reaches terminal velocity?
The weight of the falling body is equal to air resistance.
How does the weight of a falling body compare with the air resistance it encounters before it reaches terminal velocity?
The weight of the falling body is greater than air resistance.
Consider the two forces acting on the person who stands still, namely, the downward pull of gravity and the upward support of the floor. Are these forces equal and opposite? Do they form an action-reaction pair? Why or why not?
Yes. No. ASK ABOUT THIS ONE.
Free fall is motion in which gravity is the only force acting. Is a satellite circling the Earth above the atmosphere in free fall? Explain.
Yes. It is responding to gravity freely and has no other opposing forces acting on it.
Is gravitational force acting on a person who falls off a cliff? Is gravitational force acting on an astronaut inside the orbiting space shuttle?
Yes. Yes.
If the Earth were of uniform density, would your weight increase or decrease at the bottom of a deep mine shaft? Defend.
Your weight would be less in the mineshaft. ASK ABOUT EXPLAINATION
At which of the indicated positions does the satellite in elliptical orbit experience the greatest gravitational force? At which of the indicated positions does the satellite have the greatest speed? At which of the indicated positions does the satellite have the greatest velocity? At which of the indicated positions does the satellite have the greatest momentum? At which of the indicated positions does the satellite have the greatest kinetic energy? At which of the indicated positions does the satellite have the greatest gravitational potential energy? At which of the indicated positions does the satellite have the greatest total energy? At which of the indicated positions does the satellite have the greatest angular momentum? At which of the indicated positions does the satellite have the greatest acceleration? See diagram on HW #7
a a a a a c all all a
If a Mack truck and a Ford Escort have a head-on collision, which vehicle will experience the greater force of impact? Which vehicle will experience the greater impulse? Which vehicle will experience the greater change in momentum? Which vehicle will experience the greater acceleration?
both experience the same force. both experience the same impulse. both experience the same changes in momentum. the Ford Escort.
In the absence of air resistance, a ball thrown vertically upward with a certain initial KE will return to its original level with the same KE. When air resistance is a factor affecting the ball, will it return to its original level with the same, less, or more KE? Does your answer contradict the law of energy conservation? Defend.
less KE. Energy is not created nor destroyed, therefore we cannot end up with more KE in the end. With energy being transferred due to air resistance, the ball itself will have less KE in the end, but in the end, the total energy will be the same.
Which planets have a greater period than 1 Earth year, those closer to the sun than Earth or those farther from the sun than Earth?
planets farther from the sun