Question 1

A soccer ball hits a wall. In the process, the place where the ball meets the wall is pushed about $5 \mathrm{~cm}$ toward the ball's center. Is the work done on the ball by the contact interaction between it and the wall positive, negative, or zero?

Accepted Answer

The work done on the ball by the contact interaction between it and the wall is zero because the force is perpendicular to the displacement.

Question 2

In the situation described in problem C10T.5, will the car's internal energy increase, decrease, or remain unchanged? (Be prepared to explain your answer in terms of the momentum requirement and the work done.)

Accepted Answer

The car's internal energy will increase due to the work done on it. When a force is applied to stop the car, work is done on the car, converting kinetic energy into internal energy, typically in the form of heat due to friction. This process does not violate the conservation of momentum, as the momentum is transferred to the Earth, but the Earth's massive size makes its movement negligible.

Question 3

A person who exerts a 100-N force horizontally in the $+x$ direction on a wall for 10 minutes does positive work on the wall.

Accepted Answer

Work is defined as the product of the force applied and the displacement of the object in the direction of the force. Since the wall does not move, there is no displacement, and therefore, no work is done on the wall.

Question 4

A person squeezes a balloon horizontally with both hands while holding it at rest, decreasing its width by a certain amount. Is the work done on the balloon by the person positive, negative, or zero?

Accepted Answer

When a person squeezes a balloon, they apply a force over a distance, which means work is done on the balloon. The direction of the force and the direction of the displacement are the same (inward), making the work positive.

Question 5

An external interaction exerts a force $\vec{F}$ on a certain system as the place where the force is applied moves a displacement $\overrightarrow{d r}=[d x, d y, d z]$. Which of the following is the correct component expression for the work done by the interaction on the system?

Accepted Answer

The work done by a force during a displacement is given by the dot product of the force vector and the displacement vector, which is $W=F_{x} d x+F_{y} d y+F_{z} d z$. This formula represents the scalar quantity of work, summing the products of the components of force and displacement in each direction.

Question 6

When an object slides down a frictionless incline, the contact interaction between the object and incline does no work on the object

Accepted Answer

Since there is no friction, the only force acting perpendicular to the motion does no work, as work is calculated based on the component of force in the direction of motion.

Question 7

What type of interaction is involved?
A. A tension interaction
B. An electrostatic interaction
C. A friction interaction
D. A compression interaction
E. Other (specify)

Accepted Answer

An electrostatic interaction is involved because the two objects are charged and exert a force on each other due to their electric charges.

Question 8

When an object slides down a frictionless incline, The interaction does not change the object's kinetic energy

Accepted Answer

As an object slides down a frictionless incline, its potential energy is converted into kinetic energy, thereby increasing the object's kinetic energy.

Question 9

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if
-we consider the system to be the ball or

Accepted Answer

The ball's gravitational interaction with the Earth does work on the system as it causes the ball to move in a vertical direction, converting potential energy into kinetic energy and vice versa. The tension in the string only changes the direction of the ball's motion, not its energy.

Question 10

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if
-we consider the system to be the ball and the earth?

Accepted Answer

The answer of Suppose we use a string to suspend...

Question 11

A heavy ball swings at the end of a chain connected to a hook in the ceiling. Suppose I pull the ball away from its equilibrium position, hold it against my nose (with the chain taut), and then release the ball from rest. The ball swings away and then back toward my face. As long as I don't move, and the ball is left alone, I can be confident that the ball will not smash my nose

Accepted Answer

Due to the conservation of mechanical energy in a system where only conservative forces are acting, the ball cannot swing back to a position higher than its initial release point if no external work is done on the system.

Question 12

A given object always has a specific moment of inertia $l$, independent of the axis around which it rotates (as long as the axis goes through the object's center of mass)

Accepted Answer

The moment of inertia of an object depends on the axis about which it is rotating. Different axes through the object's center of mass will generally yield different moments of inertia.

Question 13

Which of the six objects shown below has the largest rotational energy? (All have the same mass.)
A.
  
B.
  
C.
  
D.
  
E.

Accepted Answer

The answer of Which of the six objects shown below...

Question 14

Two wheels have the same total mass $M$ and radius $R$. One wheel is a uniform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to a small hub. Which likely has the larger moment of inertia?

Accepted Answer

The wheel with spokes likely has a larger moment of inertia because more of its mass is distributed farther from the axis of rotation, increasing its resistance to changes in rotational motion.

Question 15

Suppose we take a disk of radius $R$ and remove the material from $r=0$ to $r=\frac{1}{2} R$, making a hole at the center of the disk. Note that this decreases the mass of the disk. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?

Accepted Answer

Removing material from the center of the disk increases the moment of inertia since mass is distributed further from the axis of rotation. The moment of inertia is directly related to $\alpha$, the angular acceleration, for a given torque. Therefore, with a higher moment of inertia, the same torque will produce a smaller angular acceleration, implying that the original object had a higher $\alpha$ due to its lower moment of inertia.

Question 16

Suppose we take a disk of radius $R$ and remove the material from $r=\frac{1}{2} R$ outward. Note that this decreases both the disk's mass and its radius. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?

Accepted Answer

The value of $\alpha$, which represents the moment of inertia factor for a disk, is determined by the distribution of mass relative to the axis of rotation. For a solid disk, $\alpha$ is $\frac{1}{2}$, regardless of changes in mass or radius, as long as the mass remains uniformly distributed. Removing material from the outer part of the disk does not change this distribution pattern relative to the axis, hence $\alpha$ remains the same.

Question 17

Suppose you have a spool of thread that can rotate around a fixed axis as you pull thread off it. If you pull the thread with your hand so that the thread always lies along a certain fixed line, how will your hand's speed as it moves compare to $|\vec{\omega}|$, where $R$ is the spool's radius and $R|\vec{\omega}|$ is angular speed?

Accepted Answer

The hand's speed will be equal to $R|\vec{\omega}|$ because the linear speed of the thread being pulled off the spool is directly related to the angular speed of the spool by the equation $v = R\omega$, where $v$ is the linear speed of the thread (or the hand's speed in this context), $R$ is the radius of the spool, and $\omega$ is the angular speed of the spool.

Question 18

Suppose we launch a disk so it rolls without slipping up an incline. The disk of course slows down as it moves up the incline. But in what direction does the friction force acting on the disk point?

Accepted Answer

The friction force points up the incline because it opposes the direction of slipping. As the disk rolls up the incline without slipping, static friction acts in the direction opposite to the potential slipping direction, which would be down the incline, thus the friction force points up the incline to prevent slipping and support rolling motion.

Question 19

As the disk rolls up the incline in the situation described in the previous problem, the friction force acting on the disk does

Accepted Answer

Friction does no work on the disk as it rolls without slipping because the point of contact between the disk and the surface does not move relative to the surface (the velocity of the point of contact is zero), so there is no displacement in the direction of the friction force.

Question 20

Suppose we put a ball at rest on a rug and then start pulling the rug out from under the ball in a certain direction. The ball rolls without slipping on the rug as the rug moves under it. The friction force that the contact interaction between the rug and ball exerts on the ball does

Accepted Answer

The friction force between the rug and the ball acts in the direction of the rug's movement, which is the same direction the ball moves. Since the force and the ball's displacement are in the same direction, the work done by friction on the ball is positive.

Quiz 1: Conservation Laws Constrain Interactions

A soccer ball hits a wall. In the process, the place where the ball meets the wall is pushed about $5 \mathrm{~cm}$ toward the ball's center. Is the work done on the ball by the contact interaction between it and the wall positive, negative, or zero?

In the situation described in problem C10T.5, will the car's internal energy increase, decrease, or remain unchanged? (Be prepared to explain your answer in terms of the momentum requirement and the work done.)

A person who exerts a 100-N force horizontally in the $+x$ direction on a wall for 10 minutes does positive work on the wall.

A person squeezes a balloon horizontally with both hands while holding it at rest, decreasing its width by a certain amount. Is the work done on the balloon by the person positive, negative, or zero?

An external interaction exerts a force $\vec{F}$ on a certain system as the place where the force is applied moves a displacement $\overrightarrow{d r}=[d x, d y, d z]$ . Which of the following is the correct component expression for the work done by the interaction on the system?

When an object slides down a frictionless incline, the contact interaction between the object and incline does no work on the object

What type of interaction is involved? A. A tension interaction B. An electrostatic interaction C. A friction interaction D. A compression interaction E. Other (specify)

When an object slides down a frictionless incline, The interaction does not change the object's kinetic energy

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if -we consider the system to be the ball or

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if -we consider the system to be the ball and the earth?

A given object always has a specific moment of inertia $l$ , independent of the axis around which it rotates (as long as the axis goes through the object's center of mass)

Which of the six objects shown below has the largest rotational energy? (All have the same mass.) A. B. C. D. E.

Two wheels have the same total mass $M$ and radius $R$ . One wheel is a uniform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to a small hub. Which likely has the larger moment of inertia?

Suppose we take a disk of radius $R$ and remove the material from $r=0$ to $r=\frac{1}{2} R$ , making a hole at the center of the disk. Note that this decreases the mass of the disk. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?

Suppose we take a disk of radius $R$ and remove the material from $r=\frac{1}{2} R$ outward. Note that this decreases both the disk's mass and its radius. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?

Suppose we launch a disk so it rolls without slipping up an incline. The disk of course slows down as it moves up the incline. But in what direction does the friction force acting on the disk point?

As the disk rolls up the incline in the situation described in the previous problem, the friction force acting on the disk does

Suppose we put a ball at rest on a rug and then start pulling the rug out from under the ball in a certain direction. The ball rolls without slipping on the rug as the rug moves under it. The friction force that the contact interaction between the rug and ball exerts on the ball does

Quiz 1: Conservation Laws Constrain Interactions

A soccer ball hits a wall. In the process, the place where the ball meets the wall is pushed about 5 cm5 \mathrm{~cm}5 cm toward the ball's center. Is the work done on the ball by the contact interaction between it and the wall positive, negative, or zero?

In the situation described in problem C10T.5, will the car's internal energy increase, decrease, or remain unchanged? (Be prepared to explain your answer in terms of the momentum requirement and the work done.)

A person who exerts a 100-N force horizontally in the +x+x+x direction on a wall for 10 minutes does positive work on the wall.

A person squeezes a balloon horizontally with both hands while holding it at rest, decreasing its width by a certain amount. Is the work done on the balloon by the person positive, negative, or zero?

When an object slides down a frictionless incline, the contact interaction between the object and incline does no work on the object

What type of interaction is involved? A. A tension interaction B. An electrostatic interaction C. A friction interaction D. A compression interaction E. Other (specify)

When an object slides down a frictionless incline, The interaction does not change the object's kinetic energy

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if -we consider the system to be the ball or

Suppose we use a string to suspend a ball from a hook in the ceiling. As the ball swings back and forth, which interaction does work on the system if -we consider the system to be the ball and the earth?

A given object always has a specific moment of inertia lll , independent of the axis around which it rotates (as long as the axis goes through the object's center of mass)

Which of the six objects shown below has the largest rotational energy? (All have the same mass.) A. B. C. D. E.

Two wheels have the same total mass MMM and radius RRR . One wheel is a uniform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to a small hub. Which likely has the larger moment of inertia?

Suppose we take a disk of radius RRR and remove the material from r=12Rr=\frac{1}{2} Rr=21​R outward. Note that this decreases both the disk's mass and its radius. Will the value of α\alphaα for the new object be larger, smaller, or the same as that for the original object?

Suppose we launch a disk so it rolls without slipping up an incline. The disk of course slows down as it moves up the incline. But in what direction does the friction force acting on the disk point?

As the disk rolls up the incline in the situation described in the previous problem, the friction force acting on the disk does

Suppose we put a ball at rest on a rug and then start pulling the rug out from under the ball in a certain direction. The ball rolls without slipping on the rug as the rug moves under it. The friction force that the contact interaction between the rug and ball exerts on the ball does

A soccer ball hits a wall. In the process, the place where the ball meets the wall is pushed about $5 \mathrm{~cm}$ toward the ball's center. Is the work done on the ball by the contact interaction between it and the wall positive, negative, or zero?

A person who exerts a 100-N force horizontally in the $+x$ direction on a wall for 10 minutes does positive work on the wall.

A given object always has a specific moment of inertia $l$ , independent of the axis around which it rotates (as long as the axis goes through the object's center of mass)

Two wheels have the same total mass $M$ and radius $R$ . One wheel is a uniform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to a small hub. Which likely has the larger moment of inertia?

Suppose we take a disk of radius $R$ and remove the material from $r=\frac{1}{2} R$ outward. Note that this decreases both the disk's mass and its radius. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?