Question 1

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

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 2

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?

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 3

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 $65.0 \mathrm {~N}$

Accepted Answer

The net work done by friction is calculated using the formula $ W = f_k \cdot d $, where $ f_k $ is the kinetic friction force and $ d $ is the distance traveled. The friction force $ f_k = \mu_k \cdot N = 0.25 \cdot 65.0 \mathrm{~N} = 16.25 \mathrm{~N} $. The distance $ d $ is the circumference of the circle, $ 2\pi \times 1.82 \mathrm{~m} \approx 11.43 \mathrm{~m} $. Thus, the work done by friction is $ 16.25 \mathrm{~N} \times 11.43 \mathrm{~m} \approx 190 \mathrm{~J} $.

Question 4

When is the angular momentum of a system constant?

Accepted Answer

According to the conservation of angular momentum principle, the total angular momentum of a system remains constant when there is no net external torque acting on the system. This means that the sum of the angular momenta of all the individual particles or components of the system remains constant.

Question 5

A stone with a mass of 1.0 kg is tied to the end of a light string which keeps it moving in a circle with a constant speed of 4.0 m/s on a perfectly smooth horizontal tabletop. The radius of the path is 0.60 m. How much work does the tension in the string do on the stone as it makes one-half of a complete circle?

Accepted Answer

The tension in the string is always perpendicular to the direction of motion, so it does no work on the stone. The work done on the stone comes from the force of gravity acting on it as it moves vertically upward along the circular path, but since it is only moving half a circle, the net work done on the stone is zero. Therefore, the answer is 0 J.

Question 6

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?

Accepted Answer

Work done by Matthew = force x distance x cos(theta)

where force = 60.0 N, distance = 12.0 m, and theta = 37.0°

Work done by Matthew = 60.0 x 12.0 x cos(37.0°)

Work done by Matthew = 575 J

Question 7

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

Accepted Answer

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

Question 8

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.)

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 9

A person carries a 2.00-N pebble through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 6.75 min. How much work did gravity do on the rock between A and B?

Accepted Answer

The answer of A person carries a 2.00-N pebble through...

Question 10

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 11

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?

Accepted Answer

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

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 its final kinetic energy is:$$K_f = \frac{1}{2}mv^2 = \frac{1}{2}(425 	ext{ kg})(1.8 	ext{ m/s})^2 = 3.2 	imes 10^5 	ext{ J}$$Therefore, the work done by the crane is:$$W = K_f - K_i = 3.2 	imes 10^5 	ext{ J} - 0 = 3.2 	imes 10^5 	ext{ J}$$

Question 13

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 $15 \mathrm {~m} ,$ what is the tension in the strap?

Accepted Answer

The work done by the strap is equal to the force applied times 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 14

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

Accepted Answer

The angular velocity of the sphere at the bottom of the incline depends only on the radius of the sphere. This is because the kinetic energy of the rolling motion is proportional to the square of the radius, while the potential energy is proportional to the height of the incline. Therefore, the ratio of kinetic to potential energy depends only on the radius, and hence the angular velocity at the bottom of the incline is also determined solely by the radius. The mass of the sphere does not affect the result because it cancels out in the calculation of the ratio of kinetic to potential energy.

Question 15

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?

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.

Question 16

A 2.0-kg object is lifted vertically through 3.00 m by a 150-N force. How much work is done on the object by gravity during this process?

Accepted Answer

The answer of A 2.0-kg object is lifted vertically through...

Question 17

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 $828 \mathrm {~N} ,$ how long is the stake?

Accepted Answer

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

Question 18

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?

Accepted Answer

When carrying the bag at a constant speed horizontally, the force exerted is perpendicular to the direction of motion, resulting in no work done.

Question 19

A person carries a 25.0-N rock through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 1.50 min. How much work did gravity do on the rock between A and B?

Accepted Answer

The answer of A person carries a 25.0-N rock through...

Question 20

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?

Accepted Answer

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

Quiz 10: Energy and Work

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 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?

Find the net work done by friction on a box that moves in a complete circle of radius 1.82 m1.82 \mathrm {~m}1.82 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 N65.0 \mathrm {~N}65.0 N

When is the angular momentum of a system constant?

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 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 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 person carries a 2.00-N pebble through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 6.75 min. How much work did gravity do on the rock between A and B?

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?

How much work would a child do while pulling a 12-kg wagon a distance of 4.3 m4.3 \mathrm {~m}4.3 m with a 22 N22 \mathrm {~N}22 N force?

A crane lifts a 425 kg steel beam vertically upward a distance of 95 m.95 \mathrm {~m} .95 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 traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 555 J555 \mathrm {~J}555 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m,15 \mathrm {~m} ,15 m, what is the tension in the strap?