Solved: Consider a ball at rest in the middle of a toy

Problem 43E A child learns in school that Earth is traveling faster than 100,000 kilometers per hour around the Sun and, in a frightened tone, asks why we aren’t swept off. What is your explanation?

Problem 47E The smokestack of a stationary toy train consists of a vertical spring gun that shoots a steel ball a meter or so straight into the air—so straight that the ball always falls back into the smokestack. Suppose the train moves at constant speed along the straight track. Do you think the ball will still return to the smokestack if shot from the moving train? What if the train gains speed along the straight track? What if it moves at a constant speed on a circular track? Why do your answers differ?

Problem 48E Consider an airplane that flies due east on a trip, then returns flying due west. Flying in one direction, the plane flies with Earth’s rotation, and in the opposite direction, against Earth’s rotation. But, in the absence of winds, the times of flight are equal either way. Why is this so?

A space probe may be carried by a rocket into outer space. What keeps the probe moving after the rocket no longer pushes it?

Problem 46E If you toss a coin straight upward while riding in a train, where does the coin land when the motion of the train is uniform along a straight-line track? When the train slows while the coin is in the air? When the train is turning?

Problem 45E Because Earth rotates once every 24 hours, the west wall in your room moves in a direction toward you at a linear speed that is probably more than 1000 kilometers per hour (the exact speed depends on your latitude). When you stand facing the wall, you are carried along at the same speed, so you don’t notice it. But when you jump upward, with your feet no longer in contact with the floor, why doesn’t the high-speed wall slam into you?

Problem 41E Two people each pull with 300 N on a rope in a tug of war. What is the net force on the rope? How much force is exerted on each person by the rope?

Problem 42E Two forces act on a parachutist falling in air: weight and air drag. If the fall is steady, with no gain or loss of speed, then the parachutist is in dynamic equilibrium. How do the magnitudes of weight and air drag compare?

Consider a crate at rest on a factory floor. As a pair of workmen begin lifting it, does the support force on the crate provided by the floor increase, decrease, or remain unchanged? What happens to the support force on the workmen’s feet?

Problem 39E In order to slide a heavy cabinet across the floor at constant speed, you exert a horizontal force of 600 N. Is the force of friction between the cabinet and the floor greater than, less than, or equal to 600 N? Defend your answer.

Problem 38E If you pull horizontally on a crate with a force of 200 N, it slides across the floor in dynamic equilibrium. How much friction is acting on the crate?

Problem 37E An empty jug of weight ?W rests on a table. What is the support force exerted on the jug by the table? What is the support force when water of weight ?w is poured into the jug?

Place a heavy book on a table and the table pushes up on the book. Why doesn’t this upward push cause the book to rise from the table?

Problem 36E As you stand on a floor, does the floor exert an upward force against your feet? How much force does it exert? Why are you not moved upward by this force?

Problem 34E When you push downward on a book at rest on a table, you feel an upward force. Does this force depend on friction? Defend your answer.

Problem 33E Consider the normal force on a book at rest on a tabletop. If the table is tilted so that the surface forms an inclined plane, will the magnitude of the normal force change? If so, how?

Problem 32E How many significant forces act on a book at rest on a table? Identify the forces.

Problem 31E A force of gravity pulls downward on a book on a table. What force prevents the book from accelerating downward?

Problem 30E If the strong man in the exercise 1 exerts a downward force of 800 N on the rope, how much upward force is exerted on the block? Exercise 1 For the pulley system shown, what is the upper limit of weight the strong man can lift?

Problem 28E Harry the painter swings year after year from his bosun’s chair. His weight is 500 N and the rope, unknown to him, has a breaking point of 300 N. Why doesn’t the rope break when he is supported as shown at the left? One day, Harry is painting near a flagpole, and, for a change, he ties the free end of the rope to the flagpole instead of to his chair, as shown at the right. Why did Harry end up taking his vacation early?

Problem 29E For the pulley system shown, what is the upper limit of weight the strong man can lift?

Problem 27E Nellie Newton hangs at rest from the ends of the rope as shown. How does the reading on the scale compare with her weight?

Problem 26E Can you say that no force acts on a body at rest? Or is it correct to say that no ?net force acts on it? Defend your answer.

Problem 25RQ What did Aristotle fail to recognize about the rules of nature for objects on Earth and in the heavens?

A hockey puck slides across the ice at a constant speed. Is it in equilibrium? Why or why not?

Problem 24RQ Stand next to a wall that travels at 30 km/s relative to the Sun. With your feet on the ground, you also travel the same 30 km/s. Do you maintain this speed when your feet leave the ground? What concept supports your answer?

Problem 23RQ A bird sitting in a tree is traveling at 30 km/s relative to the faraway Sun. When the bird drops to the ground below, does it still go 30 km/s, or does this speed become zero?

Problem 23E Can an object be in mechanical equilibrium when only a single force acts on it? Explain.

Problem 24E When a ball is tossed straight up, it momentarily comes to a stop at the top of its path. Is it in equilibrium during this brief moment? Why or why not?

Problem 22RQ What concept was missing in people’s minds in the 16th century when they couldn’t believe Earth was moving?

Problem 22E A monkey hangs stationary at the end of a vertical vine. What two forces act on the monkey? Which, if either, is greater?

Problem 21RQ If you push on a crate with a force of 100 N and it slides at constant velocity, how much is the friction acting on the crate?

Problem 21E When any object is in mechanical equilibrium, what can be correctly said about all the forces that act on it? Must the net force necessarily be zero?

Problem 20RQ What is the test for whether or not a moving object is in equilibrium?

Problem 20E Consider a pair of forces, one having a magnitude of 20 N and the other a magnitude of 12 N. What maximum net force is possible for these two forces? What is the minimum net force possible?

A bowling ball at rest is in equilibrium. Is the ball in equilibrium when it moves at constant speed in a straight-line path?

Problem 19E Start a ball rolling down a bowling alley and you’ll find that it moves slightly slower with time. Does this violate Newton’s law of inertia? Defend your answer.

Problem 18RQ When you stand at rest on a bathroom scale, how does your weight compare with the support force by the scale?

Problem 18E Each bone in the chain of bones forming your spine is separated from its neighbors by disks of elastic tissue. What happens, then, when you jump heavily onto your feet from an elevated position? (?Hint: Think about the hammerhead in Figure 2.5.) Can you think of a reason why you are a little taller in the morning than at night?

Problem 17RQ Consider a book that weighs 15 N at rest on a flat table. How many newtons of support force does the table provide? What is the net force on the book in this case?

Problem 17E When you push a cart, it moves. When you stop pushing, it comes to rest. Does this violate Newton’s law of inertia? Defend your answer.

Problem 16RQ State the equilibrium rule in symbolic notation.

Problem 16E Suppose that you’re in a moving car and the motor stops running. You step on the brakes and slow the car to half speed. If you release your foot from the brakes, will the car speed up a bit, or will it continue at half speed and slow due to friction? Defend your answer.

Problem 1E A ball rolling along a floor doesn’t continue rolling indefinitely. Is it because it is seeking a place of rest or because some force is acting upon it? If the latter, identify the force.

Lucy Lightfoot stands with one foot on one bathroom scale and her other foot on a second bathroom scale. Each scale reads 350 N. What is Lucy’s weight?

Problem 2E Copernicus postulated that Earth moves around the Sun (rather than the other way around), but he was troubled about the idea. What concepts of mechanics was he missing (concepts later introduced by Galileo and Newton) that would have eased his doubts?

Problem 2P Henry Heavyweight weighs 1200 N and stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

Problem 2RQ What class of motion, natural or violent, did Aristotle attribute to motion of the Moon?

Problem 1RQ Contrast Aristotle’s ideas of natural motion and violent motion.

Problem 1R The weights of Burl, Paul, and the scaffold produce tensions in the supporting ropes. Rank the tension in the ?left rope, from most to least, in the three situations, A, B, and C.

Problem 2R Rank the net force on the block from least to most in the four situations, A, B, C, and D.

Problem 3P The sketch shows a painter’s scaffold in mechanical equilibrium. The person in the middle weighs 500 N, and the tensions in each rope are 400 N. What is the weight of the scaffold?

Problem 3E What Aristotelian idea did Galileo discredit in his fabled Leaning lower demonstration?

Problem 3RQ What state of motion did Aristotle attribute to Earth?

Problem 3R Different materials, A, B, C, and D, rest on a table. a. From greatest to least, rank them by how much they resist being set into motion. b. From greatest to least, rank them by the support (normal) force the table exerts on them.

What Aristotelian idea did Galileo demolish with his experiments with inclined planes?

Problem 4P A different scaffold that weighs 400 N supports two painters, one 500 N and the other 400 N. The reading in the left scale is 800 N. What is the reading in the right-hand scale?

Problem 4R Three pucks, A, B, and C, are shown sliding across ice at the noted speeds. Air and ice friction forces are negligible. a. Rank them, from greatest to least, by the force needed to keep them moving. b. Rank them, from greatest to least, by the force needed to stop them in the same time interval.

Problem 4RQ What relationship between the Sun and Earth did Copernicus formulate?

Problem 5E Was it Galileo or Newton who first proposed the concept of inertia?

Problem 5RQ What did Galileo discover in his legendary experiment on the Leaning Tower of Pisa?

Problem 6E Asteroids have been moving through space for billions of years. What keeps them moving?

Problem 6RQ What did Galileo discover about moving bodies and force in his experiments with inclined planes?

Problem 7E A space probe may be carried by a rocket into outer space. What keeps the probe moving after the rocket no longer pushes it?

Problem 7RQ What does it mean to say that a moving object has inertia? Give an example.

In answer to the question “What keeps Earth moving around the Sun?” a friend asserts that inertia keeps it moving. Discuss and correct your friend’s erroneous assertion.

Problem 8RQ Is inertia the ?reason for moving objects maintaining motion or the ?name given to this property?

Problem 9E Your friend says that inertia is a force that keeps things in their place, either at rest or in motion. Do you agree? Why or why not?

Problem 9RQ Cite Newton’s first law of motion.

Problem 10E Why is it important that Tim pull slightly downward when he attempts to whip the cloth from beneath the dishes? (What occurs if he pulls slightly upward?)

Problem 11E Consider a ball at rest in the middle of a toy wagon. When the wagon is pulled forward, the ball rolls against the back of the wagon. Interpret this observation in terms of Newton’s first law.

Problem 10RQ What is the net force on a cart that is pulled to the right with 100 pounds and to the left with 30 pounds?

What class of motion, natural or violent, did Aristotle attribute to motion of the Moon?

What state of motion did Aristotle attribute to Earth?

What relationship between the Sun and Earth did Copernicus formulate?

What did Galileo discover in his legendary experiment on the Leaning Tower of Pisa?

What did Galileo discover about moving bodies and force in his experiments with inclined planes?

Is inertia the reason for moving objects maintaining motion or the name given to this property?

How does Newton’s first law of motion relate to Galileo’s concept of inertia?

What type of path does a moving object follow in the absence of a force?

What is the net force on a cart that is pulled to the right with 100 pounds of force and to the left with 30 pounds of force?

Why do we say that force is a vector quantity?

According to the parallelogram rule, what quantity is represented by the diagonal of a constructed parallelogram?

What is the resultant of a pair of 1-pound forces at right angles to each other?

Consider Nellie hanging at rest in Figure \(2.11\). If the ropes were vertical, with no angle involved, what would be the tension in each rope? Equation Transcription: Text Transcription: 2.11

Can force be expressed in units of pounds and also in units of newtons?

What is the net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left?

What is the net force on a bag pulled down by gravity with a force of 18 newtons and pulled upward by a rope with a force of 18 newtons?

What does it mean to say something is in mechanical equilibrium?

State the equilibrium rule for forces in symbolic notation.

Consider a book that weighs 15 N at rest on a flat table. How many newtons of support force does the table provide? What is the net force on the book in this case?

When you stand at rest on a bathroom scale, how does your weight compare with the support force by the scale?

A bowling ball at rest is in equilibrium. Is the ball in equilibrium when it moves at constant speed in a straight-line path?

What is the net force on an object in either static or dynamic equilibrium?

If you push on a crate with a force of 100 N and it slides at constant velocity, how great is the friction acting on the crate?

What concept was not understood in the 16th century when people couldn’t conceive of a moving Earth?

A bird sitting in a tree is traveling at 30 km/s relative to the faraway Sun. When the bird drops to the ground below, does it still move at 30 km/s, or does this speed become zero?

Stand next to a wall that travels at 30 km/s relative to the Sun. With your feet on the ground, you also travel at the same 30 km/s. Do you maintain this speed when your feet leave the ground? What concept supports your answer?

Lucy Lightfoot stands with one foot on one bathroom scale and her other foot on a second bathroom scale. Each scale reads 350 N. What is Lucy’s weight?

Henry Heavyweight weighs 1200 N and stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

The sketch shows a painter’s scaffold in mechanical equilibrium. The person in the middle weighs 500 N, and the tensions in each rope are 400 N. What is the weight of the scaffold?

A different scaffold that weighs \(400 N\) supports two painters, one \(500 N\) and the other \(400 N\). The reading in the left scale is \(800 N\). What is the reading in the right-hand scale? Equation Transcription: Text Transcription: 400 N 500 N 800 N

The weights of Burl, Paul, and the scaffold produce tensions in the supporting ropes. Rank the tensions in the left rope, from most to least, in the three situations, \(A, B, \text { and } C\). Equation Transcription: Text Transcription: A, B, and C

Rank the net forces on the blocks from least to most in the four situations, \(A, B, C, \text { and } D\). Equation Transcription: Text Transcription: A, B, C, and D

Different materials, \(A, B, C, \text { and } D\), rest on a table. (a) Rank how much they resist being set into motion, from greatest to least. (b) Rank the support (normal) forces the table exerts on them, from greatest to least. Equation Transcription: Text Transcription: A, B, C, and D

Three pucks, \(A\), \(B\), and \(C\), are shown sliding across ice at the noted speeds. Air and ice friction forces are negligible. (a) Rank the forces needed to keep them moving, from greatest to least. (b) Rank the forces needed to stop them in the same time interval, from greatest to least. Equation Transcription: A B C Text Transcription: A B C

As seen from above, a stubborn stump is pulled by a pair of ropes, each with a force of \(200 \ N\), but at different angles as shown. From greatest to least, rank the net forces on the stumps. Equation Transcription: 200 N Text Transcription: 200 N

Nellie hangs motionless by one hand from a clothesline. Which side of the line, \(a\) or \(b\), has the greater tension? Equation Transcription: a b Text Transcription: a b

Knowledge can be gained by philosophical logic and also by experimentation. Which of these did Aristotle favor, and which did Galileo favor?

A ball rolling along a floor doesn’t continue rolling indefinitely. Is this because it is seeking a place of rest or because some force is acting upon it? If the latter, identify the force.

Copernicus postulated that Earth moves around the Sun (rather than the other way around), but he was troubled about the idea. What concepts of mechanics was he missing (concepts later introduced by Galileo and Newton) that would have eased his doubts?

What Aristotelian idea did Galileo discredit in his fabled Leaning Tower demonstration?

What Aristotelian idea did Galileo demolish with his experiments with inclined planes?

Was it Galileo or Newton who first proposed the concept of inertia?

Asteroids have been moving through space for billions of years. What keeps them moving?

A space probe may be carried by a rocket into outer space. What keeps the probe moving after the rocket no longer pushes it?

In doing the tablecloth pull demonstration of inertia of Figure 2.4, why is it important that you pull slightly downward when you attempt to whip the cloth from beneath the dishes? (What occurs if you pull slightly upward?)

In tearing a paper towel or plastic bag from a roll, why is a sharp jerk more effective than a slow pull?

If you’re in a car at rest that gets hit from behind, you can suffer a serious neck injury called whiplash. What does whiplash have to do with Newton’s first law?

In terms of Newton’s first law (the law of inertia), how does a car headrest help to guard against whiplash in a rear-end collision?

Why do you seem to lurch forward in a bus that suddenly slows? Why do you seem to lurch backward when the bus picks up speed? What law applies here?

Consider a pair of forces, one having a magnitude of 20 N and the other a magnitude of 12 N. What is the strongest possible net force for these two forces? What is the weakest possible net force?

When any object is in mechanical equilibrium, what can be correctly stated about all the forces that act on it? Must the net force necessarily be zero?

Which of the following are scalar quantities, which are vector quantities, and which are neither? (a) force; (b) age; (c) acceleration; (d) temperature.

What can you correctly say about a pair of vectors that add together to equal zero?

Which is more likely to break: a hammock stretched tightly between a pair of trees or one that sags more when you sit on it?

A heavy bird sits on a clothesline. Will the tension in the clothesline be greater if the line sags a lot or if it sags a little?

A monkey hangs stationary at the end of a vertical vine. What two forces act on the monkey? Which, if either, is greater?

The rope supports a lantern that weighs \(50 \ N\). Is the tension in the rope less than, equal to, or greater than \(50 \ N\)? Use the parallelogram rule to defend your answer. Equation Transcription: 50 N Text Transcription: 50 N

The rope of \(\text {Exercise} \ 56\) is repositioned as shown and still supports the \(50-N\) lantern. Is the tension in the rope less than, equal to, or greater than \(50 \ N\)? Use the parallelogram rule to defend your answer. Equation Transcription: Exercise 56 50-N 50 N Text Transcription: Exercise 56 50-N 50 N

Can an object be in mechanical equilibrium when only a single nonzero force acts on it? Explain.

A hockey puck slides across the ice at a constant speed. Is it in equilibrium? Why or why not?

When a ball is tossed straight up, it momentarily comes to a stop at the top of its path. Is it in equilibrium during this brief moment? Why or why not?

Your friend sits at rest on a chair. Can you say that no force acts on her? Or is it correct to say that no net force acts on her? Defend your answer.

Nellie Newton hangs at rest from the ends of the rope as shown. How does the reading on the scale compare with her weight?

Harry the painter swings year after year from his bosun’s chair. His weight is \(500 \ N\) and the rope, unknown to him, has a breaking point of \(300 \ N\). Why doesn’t the rope break when he is supported as shown at the left? One day, Harry is painting near a flagpole, and, for a change, he ties the free end of the rope to the flagpole instead of to his chair, as shown at the right. Why did Harry end up taking his vacation early? Equation Transcription: 500 N 300 N Text Transcription: 500 N 300 N

If the strong man in the preceding exercise exerts a downward force of 800 N on the rope, how much upward force is exerted on the block?

For the pulley system shown, what is the upper limit of weight the strong man can lift?

A force of gravity pulls downward on a book on a table. What force prevents the book from accelerating downward?

How many significant forces act on a book at rest on a table? Identify the forces.

As you stand on a floor, does the floor exert an upward force against your feet? How much force does it exert? Why aren’t you moved upward by this force?

Place a heavy book on a table and the table pushes up on the book. Why doesn’t this upward push cause the book to rise from the table?

Suppose that you jounce up and down while weighing yourself on a bathroom scale. Which varies: the upward support force or the force of gravity on you? Why is your weight reading best shown when you stand at rest on the scale?

An empty jug of weight W rests on a table. What is the support force exerted on the jug by the table? What is the support force when water of weight w is poured into the jug?

If you pull horizontally on a crate with a force of 200 N, it slides across the floor in dynamic equilibrium. How much friction is acting on the crate?

Consider a crate at rest on a factory floor. As a pair of workmen begin lifting it, does the support force on the crate provided by the floor increase, decrease, or remain unchanged? What happens to the support force on the workmen’s feet?

In order to slide a heavy cabinet across the floor at constant speed, you exert a horizontal force of 600 N. Is the force of friction between the cabinet and the floor greater than, less than, or equal to 600 N? Defend your answer.

Two people each pull with a force of 300 N on a rope in a tug-of-war. What is the net force on the rope? How much force is exerted on each person by the rope?

Two forces act on a parachutist falling in air: the force of gravity and air resistance. If the fall is steady, with no gain or loss of speed, then the parachutist is in dynamic equilibrium. How do the magnitudes of gravitational force and air resistance compare?

A child learns in school that Earth is traveling faster than 100,000 kilometers per hour around the Sun and, in a frightened tone, asks why we aren’t swept off. What is your explanation?

Your friend says that inertia is a force that keeps things in their place, either at rest or in motion. Do you and your discussion partners agree? Why or why not?

In answer to the question “What keeps Earth moving around the Sun?” a friend asserts that inertia keeps it moving. Discuss and correct your friend’s erroneous assertion.

Consider a ball at rest in the middle of a toy wagon. When the wagon is pulled forward, the ball rolls against the back of the wagon. Discuss and interpret this observation in terms of Newton’s first law.

Suppose that you’re in a moving car and the motor stops running. You step on the brakes and slow the car to half speed. If you release your foot from the brakes, will the car speed up a bit, or will it continue at half speed and slow due to friction? Defend your answer with your discussion partners.

When you push a cart, it moves. When you stop pushing, it comes to rest. Does this violate Newton’s law of inertia? Discuss and defend your answer.

Each bone in the skeletal chain of bones forming your spine is separated from its neighbors by disks of elastic tissue. What happens, then, when you jump heavily onto your feet from an elevated position? (Hint: Think about the hammerhead in Figure 2.5.) Discuss why you think you are a little taller in the morning than at night.

Start a ball rolling down a bowling alley and you’ll find that it moves slightly slower with time. Does this violate Newton’s law of inertia? Discuss and defend your answer.

Consider the normal force on a book at rest on a tabletop. If the table is tilted so that the surface forms an inclined plane, will the magnitude of the normal force change? If so, how?

When you push downward on a book at rest on a table, you feel an upward force. Does this force depend on friction? Discuss and defend your answer.

Because Earth rotates once every 24 hours, the west wall in your room moves in a direction toward you at a linear speed that is probably more than 1000 kilometers per hour (the exact speed depends on your latitude). When you stand facing the wall, you are carried along at the same speed, so you don’t notice it. But when you jump upward, with your feet no longer in contact with the floor, why doesn’t the high-speed wall slam into you?

Before the time of Galileo and Newton, some learned scholars thought that a stone dropped from the top of a tall mast of a moving ship would fall vertically and hit the deck behind the mast by a distance equal to how far the ship had moved forward while the stone was falling. In light of your understanding of Newton’s first law, what do you think about this?

If you toss a coin straight upward while riding in a train, where does the coin land when the motion of the train is uniform along a straight-line track? When the train slows while the coin is in the air?

Discuss and answer the preceding question for when the train is rounding a corner.

The smokestack of a stationary toy train consists of a vertical spring gun that shoots a steel ball a meter or so straight into the air - so straight that the ball always falls back into the smokestack. Suppose the train moves at constant speed along the straight track. Do you think the ball will still return to the smokestack if shot from the moving train? What if the train gains speed along the straight track? What if it moves at a constant speed on a circular track? Discuss why your answers differ.