Q: A person pulls a suitcase with a strap inclined at 45° to the horizontal. The tension in the strap is 20 N and the suitcase moves 100 m. How much work does the tension force do?

$$W = 20 \times 100 \times \cos 45^\circ = 1414\ \text{J}$$

Q: A 150,000 kg rocket is launched straight up with a thrust of $$4.0 \times 10^6$ N. What is its speed at a height of 500 m, neglecting air resistance and gravity?

$$v = \sqrt{2 \frac{F \Delta s}{m}} = \sqrt{2 \frac{4.0 \times 10^6$ \times 500}{150,000}} \approx 163\ \text{m/s}$$

Q: A 35 kg motor is lifted 3.0 m in 8.0 s using a rope and pulley. What is the power output if the motor is lifted at constant speed? (Use $$g = 9.8\ \text{m/s}^2)$$

$$P = \frac{mg \Delta s}{t} = \frac{35 \times 9.8 \times 3.0}{8.0} \approx 129\ \text{W}$$

Question 1

Which of the following best describes the transformation of energy when a roller coaster descends from the top of a hill?

Accepted Answer

Gravitational potential energy is transformed into kinetic energy.

Question 2

A 70 kg skier starts down a 50 m long, 10° slope with an initial speed of 2.0 m/s. Ignoring friction, what is the skier's speed at the bottom? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v_f = \sqrt{2gh + v_i^2$}$$, where $$h = 50 \sin(10^\circ)$$; $$v_f \approx 13.1\ 	ext{m/s}$$

Question 3

Which equation correctly expresses the work done by a constant force $$\vec{F}$$ acting at an angle $$	heta to $$the displacement $$\Delta \vec{r}$$?

Accepted Answer

$$W = F \Delta r \cos 	heta$$

Question 4

A person pulls a suitcase with a strap inclined at 45° to the horizontal. The tension in the strap is 20 N and the suitcase moves 100 m. How much work does the tension force do?

Accepted Answer

$$W = 20 	imes 100 	imes \cos 45^\circ = 1414\ 	ext{J}$$

Question 5

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy is a scalar quantity and depends only on the speed and mass of an object.

Question 6

A 150,000 kg rocket is launched straight up with a thrust of $$4.0 	imes 10^6$ N. What is its speed at a height of 500 m, neglecting air resistance and gravity?

Accepted Answer

$$v = \sqrt{2 \frac{F \Delta s}{m}} = \sqrt{2 \frac{4.0 	imes 10^6$ 	imes 500}{150,000}} \approx 163\ 	ext{m/s}$$

Question 7

Which scenario best illustrates the conversion of macroscopic kinetic energy into thermal energy?

Accepted Answer

A box being dragged across a carpeted floor at constant speed, causing both the box and carpet to warm up.

Question 8

What is the correct mathematical expression for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ with angle $$\alpha$$ between them?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \alpha$$

Question 9

A spring with spring constant $$k is $$stretched from equilibrium by $$\Delta s. $$According to Hooke's Law, what is the restoring force?

Accepted Answer

$$F_{Sp} = -k \Delta s$$

Question 10

Which of the following situations results in zero work being done by a force?

Accepted Answer

A force acts perpendicular to the displacement.

Question 11

A 35 kg motor is lifted 3.0 m in 8.0 s using a rope and pulley. What is the power output if the motor is lifted at constant speed? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$P = \frac{mg \Delta s}{t} = \frac{35 	imes 9.8 	imes 3.0}{8.0} \approx 129\ 	ext{W}$$

Question 12

Which of the following is NOT a dissipative force?

Accepted Answer

Gravitational force

Question 13

If a force acts on a particle and the particle moves in a straight line, which of the following statements is true regarding the work done?

Accepted Answer

Work is positive if the force and displacement are in the same direction.

Question 14

A 1500 kg car is towed from rest with a variable tension force shown in the graph (decreasing linearly from 5000 N to 0 N over 200 m). What is the car's speed after being pulled 200 m?

Accepted Answer

$$W = 	ext{area under the curve} = \frac{1}{2} 	imes 5000 	imes 200 = 500,000\ 	ext{J}$$; $$v = \sqrt{2W/m} \approx 25.8\ 	ext{m/s}$$

Question 15

Which of the following best describes the energy principle for a system with multiple objects and/or forces?

Accepted Answer

$$\Delta K_{tot} = W_{tot}$$

Question 16

What is the correct expression for the work done by a spring according to Hooke's Law when stretched from $$s_i to$$ $$s_f$$?

Accepted Answer

$$W = \frac{1}{2} k (s_i^2$ - s_f^2$)$$

Question 17

Which of the following is true about the power delivered to a particle by a constant force $$\vec{F}$$?

Accepted Answer

$$P = \vec{F} \cdot \vec{v} = Fv \cos 	heta$$

Question 18

Which of the following is a correct statement about energy transfer and transformation?

Accepted Answer

Energy can be transformed within a system without loss, and transferred between system and environment via work or heat.

Work, Kinetic Energy, and the Energy Principle

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