Q: A 2 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? $$(g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Q: A 10 kg suitcase is pulled with a 50 N force at an angle of $$37^\circ$$ above the floor for 20 m. What is the work done by the force parallel to the floor?

$$W = Fd\cos\theta = 50 \times 20 \times \cos 37^\circ = 50 \times 20 \times 0.8 = 800\ \mathrm{J}$$

Q: A spring with a spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Q: A 4 kg block moving at $$5\ \mathrm{m/s} on a $$frictionless surface strikes a horizontal spring with $$k = 100\ \mathrm{N/m}. $$What is the maximum compression of the spring?

$$\Delta x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{4 \times 25}{100}} = 1\ \mathrm{m}$$

Q: A 1000 kg elevator is lifted at constant speed to a height of 100 m in 50 seconds. What is the minimum power required by the motor? $$(g = 9.8\ \mathrm{m/s^2$})$$

$$P = \frac{mgh}{t} = \frac{1000 \times 9.8 \times 100}{50} = 19,600\ \mathrm{W}$$

Q: A 10 kg crate is pulled up a 15 m ramp inclined at $$36^\circ$$ above the horizontal with a constant 130 N force parallel to the ramp. What is the work done by gravity?

$$W_g = -mgd\sin\theta = -10 \times 9.8 \times 15 \times \sin 36^\circ = -864\ \mathrm{J}$$

Q: A 4 kg object is launched straight up from the ground with an initial kinetic energy of 40 J. What is the maximum height it reaches? $$(g = 10\ \mathrm{m/s^2$})$$

$$h = \frac{K}{mg} = \frac{40}{4 \times 10} = 1\ \mathrm{m}$$

Question 1

A 5 kg box is pushed with a constant horizontal force of 20 N for 2 m along a frictionless surface. How much work is done by the force?

Accepted Answer

$$W = Fd = (20)(2) = 40\ \mathrm{J}$$

Question 2

Which of the following best describes the work done by gravity when a hiker climbs a mountain along a winding path compared to a straight path of the same vertical height?

Accepted Answer

The work done by gravity depends only on the change in height, not the path taken.

Question 3

A 2 kg ball is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? $$(g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 4

A 10 kg suitcase is pulled with a 50 N force at an angle of $$37^\circ$$ above the floor for 20 m. What is the work done by the force parallel to the floor?

Accepted Answer

$$W = Fd\cos	heta = 50 	imes 20 	imes \cos 37^\circ = 50 	imes 20 	imes 0.8 = 800\ \mathrm{J}$$

Question 5

A spring with a spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 6

A 4 kg block moving at $$5\ \mathrm{m/s} on a $$frictionless surface strikes a horizontal spring with $$k = 100\ \mathrm{N/m}. $$What is the maximum compression of the spring?

Accepted Answer

$$\Delta x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{4 	imes 25}{100}} = 1\ \mathrm{m}$$

Question 7

Which of the following is a non-conservative force?

Accepted Answer

Friction

Question 8

A 1000 kg elevator is lifted at constant speed to a height of 100 m in 50 seconds. What is the minimum power required by the motor? $$(g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = \frac{mgh}{t} = \frac{1000 	imes 9.8 	imes 100}{50} = 19,600\ \mathrm{W}$$

Question 9

A 10 kg crate is pulled up a 15 m ramp inclined at $$36^\circ$$ above the horizontal with a constant 130 N force parallel to the ramp. What is the work done by gravity?

Accepted Answer

$$W_g = -mgd\sin	heta = -10 	imes 9.8 	imes 15 	imes \sin 36^\circ = -864\ \mathrm{J}$$

Question 10

A 4 kg object is launched straight up from the ground with an initial kinetic energy of 40 J. What is the maximum height it reaches? $$(g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{K}{mg} = \frac{40}{4 	imes 10} = 1\ \mathrm{m}$$

Question 11

A 3 kg box is pulled across a flat surface with a coefficient of kinetic friction $$\mu_k = 0.5. If $$the box accelerates at $$2\ \mathrm{m/s^2$}$$ over 10 m, what is the net work done on the box?

Accepted Answer

$$W_{net} = \Delta K = \frac{1}{2} m v^2$ - \frac{1}{2} m v_0$^2 = \frac{1}{2} 	imes 3 	imes (\sqrt{2 	imes 2 	imes 10})^2$ = 120\ \mathrm{J}$$

Question 12

Which of the following statements about the Work-Energy Theorem is correct?

Accepted Answer

The net work done on an object equals its change in kinetic energy: $$W_{net} = \Delta K$$

Question 13

A force vs. displacement graph for a box shows a triangle with a base of 20 m and a height of 20 N. What is the work done by the force?

Accepted Answer

$$W = \frac{1}{2} 	imes 20 	imes 20 = 200\ \mathrm{J}$$

Question 14

A 2 kg block slides on a rough surface and comes to rest after traveling 10 m. If the coefficient of friction is 0.5, what was its initial speed? $$(g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0$$ = \sqrt{2 \mu_k g d} = \sqrt{2 	imes 0.5 	imes 10 	imes 10} = 10\ \mathrm{m/s}$$

Question 15

A 1400 kg block is pulled up a $$37^\circ$$ incline at constant speed by a cable. The coefficient of kinetic friction is 0.4. If the block is pulled 60 m up the incline in 25 s, what is the power output of the cable? $$(g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = \frac{F_{cable} d}{t} = \frac{(mg\sin	heta + \mu_k mg\cos	heta) d}{t}$$

Question 16

Which of the following is true about mechanical energy in a system with only conservative forces?

Accepted Answer

Mechanical energy is conserved: $$K_i + U_i = K_f + U_f$$

Question 17

A 2 kg block is attached to a horizontal spring ($$k = 50\ \mathrm{N/m}) $$and is pulled 0.5 m from equilibrium and released from rest. What is its speed as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} x = \sqrt{\frac{50}{2}} 	imes 0.5 = 2.5\ \mathrm{m/s}$$

Question 18

A 3 kg block hangs 2 m above the floor, connected via a cable to a 4 kg block on a rough table ($$\mu = 0.5). If $$released from rest, what is the speed of the 3 kg block just before hitting the floor? $$(g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{\frac{2(m_1gh - \mu m_2$ g h)}{m_1$ + m_2$}} = \sqrt{\frac{2(3 	imes 10 	imes 2 - 0.5 	imes 4 	imes 10 	imes 2)}{3 + 4}} = 2\ \mathrm{m/s}$$

Work and Energy: Study Notes for College Physics

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