Q: A 2 kg ball is dropped from a height of 5 m. Ignoring air resistance, what is the ball’s kinetic energy just before it hits the ground? (Use $$g = 9.8 \mathrm{\ m/s^2$})$$

$$K = mgh = 2 \times 9.8 \times 5 = 98 \mathrm{\ J}$$

Q: A person pulls a suitcase 100 m with a force of 20 N at an angle of $$45^\circ$$ above the horizontal. What is the work done by the force?

$$W = F \Delta s \cos \theta = 20 \times 100 \times \cos 45^\circ = 1414 \mathrm{\ J}$$

Q: Which formula gives the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ with an angle $$\theta$$ between them?

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos \theta$$

Q: A rocket is launched straight up. If the rocket motor does $$2.0 \times 10^6$ \mathrm{\ J} of $$work to lift a $$500 \mathrm{\ kg}$$ rocket to a height of $$500 \mathrm{\ m}$$, what is the rocket’s speed at that height? (Ignore air resistance, $$g = 9.8 \mathrm{\ m/s^2$})$$

$$v = \sqrt{\frac{2(W - mgh)}{m}} = \sqrt{\frac{2(2.0 \times 10^6$ - 500 \times 9.8 \times 500)}{500}} \approx 44.7 \mathrm{\ m/s}$$

Q: A 35 kg motor is lifted 3.0 m onto a truck using a rope at constant speed. What is the minimum power output required if the lift takes 5 seconds? ($$g = 9.8 \mathrm{\ m/s^2$})$$

$$P = \frac{mgh}{t} = \frac{35 \times 9.8 \times 3.0}{5} = 205.8 \mathrm{\ W}$$

Question 1

Which of the following best describes the difference between energy transformation and energy transfer in a physical system?

Accepted Answer

Energy transformation is the conversion of energy from one type to another within a system, while energy transfer is the movement of energy between the system and its environment.

Question 2

A 2 kg ball is dropped from a height of 5 m. Ignoring air resistance, what is the ball’s kinetic energy just before it hits the ground? (Use $$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$K = mgh = 2 	imes 9.8 	imes 5 = 98 \mathrm{\ J}$$

Question 3

Which equation correctly expresses the work-energy principle for a single particle acted on by a constant force?

Accepted Answer

$$\Delta K = W = F \Delta s$$

Question 4

A person pulls a suitcase 100 m with a force of 20 N at an angle of $$45^\circ$$ above the horizontal. What is the work done by the force?

Accepted Answer

$$W = F \Delta s \cos 	heta = 20 	imes 100 	imes \cos 45^\circ = 1414 \mathrm{\ J}$$

Question 5

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy depends on both the mass and the speed of an object, but not its position.

Question 6

A box is dragged across a carpeted floor at constant speed. Which statement best describes the energy changes in the system?

Accepted Answer

The macroscopic kinetic energy remains constant, but thermal energy of the box and carpet increases due to friction.

Question 7

Which formula gives the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ with an angle $$	heta$$ between them?

Accepted Answer

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos 	heta$$

Question 8

A spring with spring constant $$k is $$stretched by a displacement $$\Delta s$$ from equilibrium. What is the work done by the spring?

Accepted Answer

$$W = -\frac{1}{2}k(\Delta s)^2$

Question 9

A rocket is launched straight up. If the rocket motor does $$2.0 	imes 10^6$ \mathrm{\ J} of $$work to lift a $$500 \mathrm{\ kg}$$ rocket to a height of $$500 \mathrm{\ m}$$, what is the rocket’s speed at that height? (Ignore air resistance, $$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$v = \sqrt{\frac{2(W - mgh)}{m}} = \sqrt{\frac{2(2.0 	imes 10^6$ - 500 	imes 9.8 	imes 500)}{500}} \approx 44.7 \mathrm{\ m/s}$$

Question 10

Which of the following is true about the work done by a force perpendicular to the displacement of an object?

Accepted Answer

No work is done because $$\cos 90^\circ = 0.$$

Question 11

A 35 kg motor is lifted 3.0 m onto a truck using a rope at constant speed. What is the minimum power output required if the lift takes 5 seconds? ($$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$P = \frac{mgh}{t} = \frac{35 	imes 9.8 	imes 3.0}{5} = 205.8 \mathrm{\ W}$$

Question 12

Which of the following best describes the effect of friction when you rub your hands together rapidly?

Accepted Answer

Friction transforms macroscopic kinetic energy into thermal energy, increasing the temperature of both hands.

Question 13

If a force $$\vec{F}$$ acts on a particle moving with velocity $$\vec{v}$$, what is the instantaneous power delivered to the particle?

Accepted Answer

$$P = \vec{F} \cdot \vec{v}$$

Question 14

A car is towed from rest over a distance of 200 m. The force applied varies with position as shown in a graph. How can the total work done be determined?

Accepted Answer

By calculating the area under the force vs. displacement graph from $$x = 0 to$$ $$x = 200 m.$$

Question 15

Which of the following is a correct statement about the conservation of energy in an isolated system?

Accepted Answer

The total energy of an isolated system remains constant over time.

Question 16

A skater pushes against a wall and rolls backwards. Which statement best explains how her kinetic energy increases?

Accepted Answer

She uses internal energy to push herself back; the wall does no work because her hands do not move.

Question 17

Which of the following is the correct expression for the kinetic energy of a single particle of mass $$m$$ and velocity $$v$$?

Accepted Answer

$$K = \frac{1}{2}mv^2$

Question 18

If multiple forces act on a single particle, how is the total work done on the particle calculated?

Accepted Answer

By summing the work done by each force individually: $$W_{	ext{tot}} = W_1$ + W_2$ + \ldots$$

Work and Kinetic Energy: Principles, Forms, and Applications

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