Question 1

A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.)
A) his total kinetic energy
B) his translational kinetic energy
C) his rotational kinetic energy
D) his angular momentum
E) his moment of inertia 
F) the horizontal component of his linear momentum
G) the location of his center of mass (or center of gravity)

Accepted Answer

The answer of A ballet dancer is spinning in the...

Question 2

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?
A) the one of smallest diameter
B) the one of greatest mass
C) the disk
D) the sphere
E) They will reach the bottom at the same time.

Accepted Answer

The sphere will reach the bottom first. This is because a sphere has a higher rotational inertia than a disk of the same mass and diameter, which means it requires more torque to rotate at the same speed. As the sphere and disk roll down the inclined plane, they both experience the same force due to gravity, but the sphere will be able to maintain a higher speed because it has a larger rotational inertia. As a result, the sphere will reach the bottom before the disk.

Question 3

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)
A) Her angular momentum remains constant.
B) Her moment of inertia remains constant.
C) Her kinetic energy remains constant.
D) She is subject to a constant non-zero torque.

Accepted Answer

CWhen the skater pulls in her arms, she reduces her moment of inertia and spins faster to conserve angular momentum (A), as no external torques act on her. The kinetic energy remains constant (C) because the work done is internal and does not add or remove energy from the system.

Question 4

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on
A) the mass of the sphere.
B) the radius of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Accepted Answer

The angular velocity of the sphere at the bottom of the incline depends only on the radius of the sphere. This can be shown by using conservation of energy and the conservation of angular momentum. The potential energy that the sphere loses as it rolls down the incline is converted into both kinetic energy of translation and kinetic energy of rotation. Since the sphere is rolling without slipping, the two kinetic energies are related by $v=\omega R$, where $v$ is the linear velocity of the center of mass and $\omega$ is the angular velocity. Using conservation of energy and the fact that the sphere starts from rest, we can find that the final velocity at the bottom of the incline is $v=\sqrt{\frac{2}{5} \frac{MgR}{I}}$, where $I$ is the moment of inertia of the sphere (which can be found using the formula for the moment of inertia of a solid sphere). Simplifying this expression, we see that the angular velocity at the bottom of the incline is $\omega=\sqrt{\frac{5g}{7R}}$. Thus, the angular velocity depends only on the radius of the sphere and not on its mass.

Question 5

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on
A) the mass of the sphere.
B) the radius of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Accepted Answer

The linear velocity of a uniform solid sphere rolling without slipping down an inclined plane, starting from rest, depends on the height of the incline and the acceleration due to gravity, but not on the mass or the radius of the sphere. This is because both the translational and rotational kinetic energies at the bottom are determined by the gravitational potential energy lost, which is independent of mass and radius for a given height.

Question 6

How much work would a child do while pulling a 12-kg wagon a distance of $4.3 \mathrm {~m}$ with a $22 \mathrm {~N}$ force?
A) 95 J
B) 52 J
C) 67 J
D) 109 J

Accepted Answer

Work done = Force × Distance = 22 N × 4.3 m = 94.6 J ≈ 95 J

Question 7

A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m.
(a) What is the work done by the 5500-N force?
(b) What is the work done by gravity?
(c) What is the net work done on the elevator?

Accepted Answer

The answer of A 500-kg elevator is pulled upward with...

Question 8

You carry a 7.0-kg bag of groceries $1.2 \mathrm {~m}$ above the ground at constant speed across a $2.7 \mathrm {~m}$ room. How much work do you do on the bag in the process?
A) 0.00 J
B) 82 J
C) 185 J
D) 157 J

Accepted Answer

Since the bag is being carried at a constant speed, there is no net force acting on it and thus no work is being done on the bag. Work is only done when there is a force and a displacement in the direction of the force. Therefore, the answer is 0 J.

Question 9

When is the angular momentum of a system constant?
A) Only when its total kinetic energy is constant.
B) Only when no net external force acts on the system.
C) Only when the linear momentum and the energy are constant.
D) Only when no net external torque acts on the system.
E) Only when the moment of inertia is constant.

Accepted Answer

The angular momentum of a system is constant only when there is no net external torque acting on the system. This means that if the system experiences an external torque, its angular momentum may change. Therefore, options A, B, C, and E are incorrect.

Question 10

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If $555 \mathrm {~J}$ of work are done by the strap while moving the suitcase a horizontal distance of $15 \mathrm {~m} \text {, }$ what is the tension in the strap?
A) 46 N
B) 37 N
C) 52 N
D) 56 N

Accepted Answer

The work done by the strap is equal to the force applied multiplied by the distance moved in the direction of the force. In this case, the distance moved in the direction of the force is the horizontal distance of 15 m. Therefore, the tension in the strap is:$$W = Fd$$$$F = \frac{W}{d} = \frac{555 \mathrm {~J}}{15 \mathrm {~m}} = 37 \mathrm {~N}$$

Question 11

Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of 37.0° above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do?
A) 185 J
B) 433 J
C) 575 J
D) 720 J

Accepted Answer

The force exerted by Matthew is at an angle, so we need to find the component of the force parallel to the displacement of the wagon:

Fcos(θ)=60.0Ncos(37.0°)=48.0N

The work done by Matthew is:

W=Fcos(θ)d=(48.0N)(12.0m)=576J

Rounding to the nearest tenth, we get:

W=575J

Therefore, the correct answer is C (575 J).

Question 12

A crane lifts a 425 kg steel beam vertically upward a distance of $95 \mathrm {~m} .$ How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces. A) 4.7 × 10⁵ J B) 2.7 × 10⁵J C) 3.2 × 10⁵ J D) 4.0 × 10^{5 J}

Accepted Answer

The work done by the crane is equal to the change in kinetic energy of the beam. The initial kinetic energy of the beam is zero, and the final kinetic energy is:$$K_f = \frac{1}{2}mv^2 = \frac{1}{2}(425 	ext{ kg})(1.8 	ext{ m/s})^2 = 729 	ext{ J}$$The work done by the crane is:$$W = K_f - K_i = 729 	ext{ J} - 0 = 729 	ext{ J}$$Therefore, the correct answer is A.

Question 13

Find the net work done by friction on a box that moves in a complete circle of radius $1.82 \mathrm {~m}$ on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is 0.25, and the box weighs $65.0 \mathrm {~N}$
A) 190 J
B) 0 J
C) 1800 J
D) 370 J

Accepted Answer

The net work done by friction is calculated using the formula $ W = f_k \cdot d $, where $ f_k = \mu_k \cdot N $ is the frictional force, $ \mu_k = 0.25 $ is the coefficient of kinetic friction, $ N = 65.0 \mathrm{~N} $ is the normal force, and $ d = 2\pi \times 1.82 \mathrm{~m} $ is the distance traveled in a circle. Calculating gives $ f_k = 0.25 \times 65.0 = 16.25 \mathrm{~N} $ and $ d = 2\pi \times 1.82 \approx 11.43 \mathrm{~m} $. Thus, $ W = 16.25 \times 11.43 \approx 185.86 \mathrm{~J} $, which rounds to 190 J.

Question 14

If the answer to your calculation has units of kg ∙ m²/s² , what type of quantity could it be? (There could be more than one correct choice.) A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque

Accepted Answer

The unit kg ∙ m²/s² is equivalent to a joule, which is a unit of work (B) and rotational kinetic energy (F). It is also equivalent to the unit of torque (H), which is force times distance.

Question 15

If the answer to your calculation has units of kg ∙ m²/s, what type of quantity could it be? (There could be more than one correct choice). A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque

Accepted Answer

Angular momentum has units of kg ∙ m²/s, which matches the given units.

Question 16

A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37° above the horizontal. How much work does gravity do on the box during this process?
A) -1100 J
B) -110 J
C) -140 J
D) -180 J
E) 120 J

Accepted Answer

Gravity does no work on the box because the force of gravity is perpendicular to the displacement of the box. The work done on the box is equal to the work done by the person pulling the box up the ramp against gravity. The calculation for this work is:

Work = force x distance x cos(theta)

where force is the component of the force vector that is parallel to the displacement, distance is the distance over which the force is applied, and theta is the angle between the force vector and the displacement.

In this case, the force is equal to the weight of the box (30 N) times the sin of the angle of the ramp (37°) because this is the component of the weight that is parallel to the ramp. The distance is equal to the length of the ramp (6.0 m), and cos(theta) is equal to the cosine of the angle of the ramp (37°). Plugging in these values, we get:

Work = (30 N) x (sin 37°) x (6.0 m) x (cos 37°) ≈ 110 J

Therefore, the correct answer is B.

Question 17

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is 
A) higher than when it was released.
B) lower than when it was released.
C) at the same height from which it was released.
D) It is impossible to tell without knowing the mass of the ball.
E) It is impossible to tell without knowing the radius of the ball.

Accepted Answer

The answer of A uniform ball is released from rest...

Question 18

A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is $4.0 \mathrm {~m}$ above the ground. What is the mass of the box?
A) 8.9 kg
B) 5.3 kg
C) 6.7 kg
D) 8.0 kg

Accepted Answer

The work done (350 J) is equal to the gravitational potential energy gained by the box, which is $mgh$. Given $h = 4.0 \, \text{m}$ and $g = 9.8 \, \text{m/s}^2$, we can solve for $m$: $350 = m \times 9.8 \times 4.0$. Solving for $m$ gives approximately 8.9 kg.

Question 19

It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is $828 \mathrm {~N} \text {, }$ how long is the stake?
A) 0.36 m
B) 0.23 m
C) 0.31 m
D) 0.41 m

Accepted Answer

Work done = Force x Distance$0.30 \times 10^3 \mathrm{~J} = 828 \mathrm{~N} \times d$$d = 0.36 \mathrm{~m}$

Question 20

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?
A) The small sphere arrives first.
B) Both reach the bottom at the same time.
C) The large sphere arrives first.

Accepted Answer

For rolling objects, the acceleration down an incline does not depend on the mass or the radius of the object but on the gravitational acceleration and the incline angle. Both spheres will have the same acceleration and thus reach the bottom at the same time.

Quiz 10: Energy and Work

A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.)

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?

A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

How much work would a child do while pulling a 12-kg wagon a distance of $4.3 \mathrm {~m}$ with a $22 \mathrm {~N}$ force?

A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. (a) What is the work done by the 5500-N force? (b) What is the work done by gravity? (c) What is the net work done on the elevator?

You carry a 7.0-kg bag of groceries $1.2 \mathrm {~m}$ above the ground at constant speed across a $2.7 \mathrm {~m}$ room. How much work do you do on the bag in the process?

When is the angular momentum of a system constant?

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If $555 \mathrm {~J}$ of work are done by the strap while moving the suitcase a horizontal distance of $15 \mathrm {~m} \text {, }$ what is the tension in the strap?

Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of 37.0° above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do?

A crane lifts a 425 kg steel beam vertically upward a distance of $95 \mathrm {~m} .$ How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

Find the net work done by friction on a box that moves in a complete circle of radius $1.82 \mathrm {~m}$ on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is 0.25, and the box weighs $65.0 \mathrm {~N}$

If the answer to your calculation has units of kg ∙ m²/s² , what type of quantity could it be? (There could be more than one correct choice.)

If the answer to your calculation has units of kg ∙ m²/s, what type of quantity could it be? (There could be more than one correct choice) .

A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37° above the horizontal. How much work does gravity do on the box during this process?

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is $4.0 \mathrm {~m}$ above the ground. What is the mass of the box?

It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is $828 \mathrm {~N} \text {, }$ how long is the stake?

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?