Physics Chapter 5

An astronaut of mass 80 kg weighs about 800 N on Earth (remember the difference!). His weight on Mars, where the acceleration due to gravity "g" becomes 3.7 m/s2, is equal to __________________________.

296 N We have to use the formula weight = mg to find the astronaut

What is the tension in a rope that is pulled by two people, each exerting 300 N of force? ____________________

300 N

If two objects, one twice as massive as the other, are pulling on a rope toward each other on a frictionless surface and are 12 m apart. They meet face to face. What is the distance the more massive person moved?

4 m (if they were the same mass, we

A vertical vector of 3 units combined with a horizontal vector of 4 units has a resultant of ______________.

5 units Use the Pythagorean theorem, which is a2 + b2 = c2. a = 3 units, and b = 4 units, so c = sqrt(32 + 42) = sqrt(25) = 5 units.

If one end of a rope is pulled by a student with a force of 50 N, while the other end is pulled by a teacher with 50 N, the tension in the rope is ________________.

50 N

A boxer can hit a heavy bag with great force. Why can't he hit a piece of tissue paper in midair with the same amount of force?

A boxer can only apply as much force to an object as the object can apply back.

How does a helicopter get its lifting force?

A helicopter gets its lifting force by pushing air downward, in which case the reaction is the air pushing the helicopter upward.

How many forces are required for an interaction?

A pair of forces are required for an interaction.

A boxer punches a sheet of paper in midair and brings it up from rest to a speed of 25 m/s in 0.05 s. What is the acceleration of the paper?

Acceleration = change in velocity/time Acceleration = (final velocity - initial velocity)/time Acceleration = (25 m/s - 0 m/s)/0.05 s Acceleration = (25 m/s)/(0.05 s) Acceleration = 500 m/s2

identify action and reaction forces: Earth gravity pulls down on a book.

Action force: Earth pulls down on a book. Reaction force: The book pulls up on the Earth.

identify action and reaction forces: A hammer hits a nail.

Action force: Hammer hits nail. Reaction force: Nail hits hammer.

identify action and reaction forces: A helicopter blade pushes air downward.

Action force: Helicopter blade pushes air downward. Reaction force: Air pushes helicopter blade upward.

Identify the action-reaction pairs of forces for the following situations: You step off a curb.

Action: Earth pulls you downward. Reaction: You pull the Earth upward. b.

Identify the action-reaction pairs of forces for the following situations: You pat your tutor on the back.

Action: You touch tutor's back. Reaction: Tutor's back touches you.

When you kick a football, what action and reaction forces are involved? Which force, if either, is greater?

Action: your foot against the ball. Reaction: the ball against your foot. Both forces have the same magnitude, according to Newton's Third Law.

Ken and Joanne are astronauts floating some distance apart in space. They are joined by a safety cord whose ends are tied around their waists. If Ken starts pulling on the cord, will he pull Joanne toward him, or will he pull himself toward Joanne, or will both astronauts move?

Both will move. Ken's pull on the rope is transmitted to Joanne, causing her to accelerate toward him. By Newton's Third Law, the rope pulls back on Ken, causing him to accelerate toward Joanne.

If there is one force present, there must be a

Faction force back

Here the stone is sliding down a friction-free incline Identify the forces that act on it

Gravity or weight is acting straight down, and the normal force is acting at an angle.

For a steeper incline, the horizontal component, parallel to the incline, is (greater / the same / less).

Greater

How great is the force of friction acting on a shoe at rest on an incline compared with the resultant of the vectors mg and N?

If the shoe is at rest, friction has to be canceled out exactly. So, when we take the resultant of the vectors mg and N, that force along the incline will be exactly equal to the force of friction

If you stand next to a wall on a frictionless skateboard and push the wall with a force of 40 N, how hard does the wall push on you? If your mass is 80 kg, show that your acceleration is 0.5 m/s2.

If you push with 40 N of force, the wall pushes back with that same 40 N of force. m = 80 kg F = 40 N Fnet = ma a = Fnet/m = (40 N)/(80 kg) = 0.5 m/s2

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 deceleration?

In accord with Newton's Third Law, the force on each will be of the same magnitude. But the effect of the force (acceleration) will be different for each because of the different mass. The more massive truck undergoes less change in motion than the Civic.

A boxer punches a sheet of paper in midair and brings it up from rest to a speed of 25 m/s in 0.05 s. If the mass of the paper is 0.003 kg, what force does the boxer exert on it?

Newton's Second Law: Fnet = ma m = 0.003 kg a = 500 m/s2 Fnet = ma = (0.003 kg)(500 m/s2) = 1.5 N

When you rub your hands together, can you push harder on one hand than the other? Why or why not?

No! Each hand pushes equally on the other according to Newton's Third Law - you cannot push harder on one hand than the other.

If the system is considered to be the apple and the orange together (see the figure below), is there a net force on the system when the apple pulls (ignoring friction with the floor)?

No, for the pair of forces are internal to the apple-orange system.

Mr. Brady challenges you and your friend to each pull on a pair of scales attached to the ends of a horizontal rope, in tug-of-war fashion, so that the readings on the scales will differ. Can this be done?

No. The net force on the rope is zero, meaning tension is the same on both ends, according to Newton's Third Law.

Suppose the string in the last question breaks and the stone slows in its upward motion. Draw a force vector diagram of the stone when it reaches the top of its path.

Now, the only force acting on the stone is gravity, down. Your diagram should show the stone with one vector, gravity.

you can

Pushes back

Why does vertically falling rain make slanted streaks on the side windows of a moving automobile? If the streaks make an angle of 45°, what does this tell you about the relative speeds of the car and the falling rain?

Rain makes slanted streaks because there

What is meant by the phrase resolving a vector?

Resolving a vector means to break the vector down into a horizontal component and a vertical component. You do this by making the vector in question the diagonal of a rectangle. The length and the width of this rectangle are your horizontal and vertical components.

What is the acceleration of the stone of the last question at the top of its path?

Since the only force involved here is gravity, the stone will accelerate at g, or 10 m/s2 down.

A rocket becomes progressively easier to accelerate as it travels through space. Discuss why this is so. (Hint: About 90% of the mass of a newly-launched rocket is fuel.)

The answer is given in Newton's Second Law: a = F/m. As fuel is burned, the mass of the rocket decreases. As m decreases and F remains the same, a increases! There is less mass to be accelerated as fuel is consumed.

As a dropped ball falls toward the surface of the Earth there is an action force pulling the ball to the ground. What is the reaction force? _____________________________________________________

The ball pulling the Earth upward.

If the forces that act on a cannonball and the recoiling cannon from which it is fired are equal in magnitude, why do the cannonball and cannon have very different accelerations?

The different acceleration are due to the different masses.

Suppose that two carts, one twice as massive as the other, fly apart when the compressed spring that joins them is released. What is the acceleration of the heavier cart relative to that of the lighter cart as they start to move apart?

The force on each cart will be the same. But since the masses are different, the accelerations will differ. The twice-as-massive cart will undergo only half the acceleration of the less massive cart.

Identify the force that propels a rocket.

The force that propels a rocket is the exhaust gases pushing on the rocket.

Two people of equal mass attempt a tug-of-war with a 12-m rope while standing on frictionless ice. When they pull on the rope, each of them slides toward the other. How do their accelerations compare, and how far does each person slide before they meet?

The forces on each are the same in magnitude, and their masses are the same, so their accelerations will be the same. They will slide an equal distance of 6 meters to meet at the midpoint.

A farmer asks his talking horse to pull a wagon. The horse refuses, saying that such an effort wouldn

The horse will still accelerate because we have to look at the forces on the horse specifically. There

Consider a baseball player batting a ball. Identify the action-reaction pairs: While the ball is in flight.

The major interactions here are with Earth's gravity and the air. Action: Earth pulls down on the ball (weight). Reaction: ball pulls up on Earth. Action: Air pushes ball. Reaction: Ball pushes air.

There are two interactions that involve a stone at rest on the ground. One is between the stone and Earth as a whole: Earth pulls down on the stone (mg) and the stone pulls up on Earth. What is the other interaction?

The other interaction is between the stone and the ground on which it rests. The stone pushes down on the ground

A boxer punches a sheet of paper in midair and brings it up from rest to a speed of 25 m/s in 0.05 s. How much force does the paper exert on the boxer?

The paper exerts the exact same force, 1.5 N, in the opposite direction!

A baseball bat is swung against a baseball, which accelerates. When the ball is caught, what produces the force on the player's glove?

The rapid deceleration (de-acceleration) of the speeding ball on the player's glove produces the force on the player's glove. We're used to saying a force produces an acceleration, but here, an acceleration (or deceleration) produces a force!

Consider hitting a baseball with a bat. If we call the force on the bat against the ball the action force, identify the reaction force.

The reaction force would be the ball against the bat.

Two 100-N weights are attached to a spring scale as shown. Does the scale read 0, 100 N, or 200 N, or does it give some other reading? (Hint: Would the reading be different if one of the ropes were tied to the wall instead of to the hanging 100-N weight?)

The scale will read 100 N, the same as it would read if one of the ends were tied to a wall instead of tied to the 100 N hanging weight. Although the net force on the system is zero, the tension in the rope within the system is 100N, as would show on the scale reading.

The stone below is at rest, interacting with both the surface of the incline and the block. Identify all the forces that act on the stone, and draw appropriate force vectors.

The stone

In a tug-of-war between Sam and Maddy, each pulls on the rope with a force of 250 N. What is the tension in the rope? If both remain motionless, what horizontal force does each exert against the ground?

The tension in the rope is 250 N. With no acceleration, each must experience a 250-N force of friction via the ground. This is provided by pushing against the ground with 250 N.

The same stone is being accelerated vertically upward. Which is the longer vector, and why?

The tension up is the longer vector. There must be a net force in the direction of the acceleration, according to Newton

A person weight and normal force usually have the same magnitude when they stand on a horizontal surface. Draw these forces.

The weight is the red vector pointing down. The normal force is the red vector pointing up. They are equal and opposite.

Which team wins in a tug-of-war: the team that pulls harder on the rope or the team that pushes harder against the ground?

The winning team pushes harder against the ground. The ground then pushes harder on them, producing a net force in their favor.

What aspect of physics was not known by the writer of this newspaper editorial that ridiculed early experiments by Robert H. Goddard on rocket propulsion above Earth's atmosphere? "Professor Goddard [...] does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react [...] he seems to lack the knowledge ladled out daily in high schools."

The writer apparently didn't know that the reaction to exhaust gases does not depend on a medium for the gases. A gun, for example, will kick if fired in a vacuum. In fact, in a vacuum there is no air drag and a bullet or rocket operates even better.

A balloon floats motionless in the air. A balloonist begins climbing the supporting cable. In which direction does the balloon move as the balloonist climbs?

To climb upward means pulling the rope downward, which moves the balloon downward as the balloonist climbs.

You hold an apple over your head. Identify all the forces acting on the apple and their reaction forces.

Two force pairs act: Earth's pull on the apple (action), and the apple's pull on the Earth (reaction). In addition, your hand pushes the apple upward (action), and the apple pushes your hand downward (reaction).

How does the magnitude of the vertical component of velocity for a ball 1 tossed at an upward angle change as the ball travels upward? How about the horizontal component of velocity when air resistance is negligible?

We know a ball slows down as we throw it into the air, until it comes to a stop at the very top of its trajectory. That means the magnitude of the vertical component of velocity will decrease. Is there any force acting horizontally when we toss a ball into the air? No! That means the horizontal component of velocity will stay the same length as the ball travels. We will see this situation in more detail if we get to projectile motion in Chapter 10.

What happens to the magnitude (length) of the normal vector on a block resting on an incline when the angle of the incline increases?

When the angle of the incline increases, the block is not pressing as hard against the surface. That means the reaction force, the normal force, won

You push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn't this mean that the forces cancel each other, making acceleration impossible? Why or why not?

When you push a car, you exert a force on the car. When the car simultaneously pushes back on you, that force is on you - not the car. You don't cancel a force on the car with a force on you. For cancellation, the forces have to be equal and opposite and act on the same object.

Identify the pair of forces involved when you push on an object with your fingers. Sketch the situation, showing the forces as vectors.

When you push on say, a wall, your hand applies a force, and the wall pushes back with an equal and opposite force.

State Newton's Third Law of Motion.

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Consider a baseball player batting a ball. Identify the action-reaction pairs: When the ball is being hit.

While the bat is in contact with the ball, there are two interactions. One with the bat, and one with Earth's gravity. Action: bat hits ball. Reaction: Ball hits bat. Action: Earth pulls down on ball (weight). Reaction: ball pulls up on Earth.

You hold an apple over your head. When you drop the apple, identify all the forces acting on it as it falls and the corresponding reaction forces. Ignore air drag.

With no air resistance, there's one pair of forces: Earth's pull on the apple (action), and the apple's pull on the Earth (reaction).

Does a baseball bat slow down when it hits a ball?

Yes, a baseball exerts an external force on the bat, opposite to the bat's motion. This external force decelerates the oncoming bat.

To produce a net force on a system, must there be an externally applied net force?

Yes, an external net force is required to accelerate the system.

If the system of the figure below is only the orange, is there a net force on the system when the apple pulls?

Yes, and that external net force accelerates the system.

Is it true that when you drop from a branch to the ground below, you pull upward on Earth? If so, then why isn't the acceleration of Earth noticed?

Yes, it's true. The Earth can't pull you downward without you simultaneously pulling Earth upward. The acceleration of Earth is really small, and not noticed, due to its enormous mass.

Consider the system of a single football. If you kick it, is there a net force to accelerate the system? If a friend kicks it at the same time with an equal and opposite force, is there a net force to accelerate the system?

Yes, the net force is provided by contact with your foot. If two opposite and equal forces act on the ball, the net force on it is zero and it will not accelerate.

A stone is suspended at rest by a string. Should your vectors have a zero resultant? Why or why not?

Yes, the vectors should sum to zero, because the stone is suspended at rest. If the stone is at rest, that means it

Earth pulls down on you with a gravitational force that you call your weight. Do you pull up on Earth with the same amount of force?

Yes, you pull upward with the same amount of force on Earth.

Can you physically touch a person without that person touching you with the same amount of force?

You cannot touch without being touched, and with the same amount of force!

Any interaction between two objects requires ____________________.

a pair of forces

The normal force that acts on a block of ice that slides on a ramp (increases, decreases, remains the same) as the slope of the ramp increases.

decreases (the normal force gets smaller and smaller; if vertical, there

For a steeper incline, the vertical component, perpendicular to the incline, (increases / stays the same / decreases).

decreases (this is the "action" force of pressing against the ramp that causes the normal force as the "reaction" force to decrease as well, as long as the ramp keeps getting steeper)

For every action force, there must be a reaction force that is ____________________________________________________________. But be careful! When a cannonball is fired from a cannon, which undergoes the greatest acceleration? ____________________________________________________

equal in magnitude and opposite in direction. The cannonball undergoes the greater acceleration, even though the force is the same on both. The cannonball has a lower mass.

The force due to gravity that acts on a block of ice that slides down an icy ramp (is less than mg, is equal to mg, is more than mg) as the angle of the ramp changes.

equal to mg (it never changes

imagine bouncing a ball against the floor. When the ball is in the air, its acceleration is equal to _______________. The force exerted on the ball to cause the bounce comes from the __________________.

g (10 m/s2); floor.

A shoe on an inclined surface does NOT slide down the ramp when friction equals the _______________________________.

horizontal component of gravity Gravity is a vector that points straight down, even if our object is on an incline. If we resolve this vector into components, we see that there is a vertical component that cancels out the normal force, and a horizontal component. If the object on a slope doesn

For an object or system to accelerate, there must be a ______________________________. The net force exerted on the tires of a car that directly accelerate it along a road is exerted by the _____________________________. For example, with no air resistance, once a tossed ball leaves your hand only the force of _______________ acts on it.

net force road gravity

Can a boxer exert a 60 N force on a piece of tissue paper? (yes / no). This is because the boxer (can / cannot) exert a force greater than the tissue paper can exert back.

no; cannot Going back to our question on the first day of the chapter, a championship boxer

You couldn

push back interaction

When a horse walks, he pushes on the ground to the left and the ground _______________________________.

pushes on the horse to the right.

As the sloped surface supporting a shoe becomes steeper: The shoe

remains the same increases This is more or less saying that as the slope gets steeper, the component of gravity along the length of the slope, which we usually call the "horizontal component" of gravity, gets longer and longer. decreases

A pair of action-reaction forces always occurs (simultaneously / at different times).

simultaneously (which means at the same time)

After a head-on collision between two different mass objects traveling at the same speed, the object that undergoes the greatest change in velocity will be the one with the _____________ mass. An aardvark and a Land Rover traveling at the same speed have a head-on collision. The one that undergoes the greatest change in velocity is the __________________.

smaller aardvark

In a tug-of-war, the winning team exerts the greatest force on (the rope / the ground).

the ground The teams MUST exert the same force on the rope, as per

The impact force between two objects is the same for both objects. An aardvark and a Land Rover traveling at the same speed collide head-on. The impact force is ____________________. A pair of carts with a compressed spring between them is set in motion. If one cart accelerates at twice the rate of the other, its mass is _____________ the mass of the other cart.

the same for both half as much as (remember F = ma! Half the mass for the same force means twice the acceleration!)

Vertically falling snow makes slanted 45-degree streaks on the side of the side window of a moving car. The speed of the car equals _________________.

the speed of the falling snow The snow makes streaks on the window at an angle because it has a horizontal component of speed (from the car) and a vertical component of speed (from the snow). If the angle is 45 degrees, those components are equal.

when your hands are in contact with each other you cannot push

with more force on one hand than the other hand pushes back with.