Q: A spring with a constant $$k = 440\ \mathrm{N/m} is $$stretched to store $$25\ \mathrm{J} of $$energy. How far is it stretched?

$$x = \sqrt{\frac{2 \times 25}{440}} \approx 0.337\ \mathrm{m}$$

Q: A 7 kg monkey swings from a branch 1.2 m above the ground. What is the change in gravitational potential energy?

$$\Delta U = mgh = 7 \times 9.8 \times 1.2 = 82.32\ \mathrm{J}$$

Q: A skier starts from rest at the top of a frictionless incline of height $$185\ \mathrm{m}$$ and angle $$35^\circ. $$What is the skier's speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 185} \approx 60.3\ \mathrm{m/s}$$

Q: A roller coaster car is released from rest at a height of $$35\ \mathrm{m}. $$What is its speed at a height of $$15\ \mathrm{m}$$, neglecting friction?

$$v = \sqrt{2g(h_1$ - h_2$)} = \sqrt{2 \times 9.8 \times (35 - 15)} \approx 19.8\ \mathrm{m/s}$$

Question 1

Which of the following best describes the work-energy theorem?

Accepted Answer

The total work done on an object is equal to its change in kinetic energy: $$W = \Delta K$$

Question 2

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2}(2)(3^2$) = 9\ \mathrm{J}$$

Question 3

Which of the following is an example of gravitational potential energy?

Accepted Answer

A book held at a height above the ground: $$U = mgh$$

Question 4

A roller coaster car of mass $$m is $$released from rest at a height $$h_1. $$Neglecting friction, what is its speed $$v_2 at a $$lower height $$h_2$$?

Accepted Answer

$$v_2$$ = \sqrt{2g($$h_1$$ - $$h_2$$)}$$

Question 5

Which of the following statements about conservative forces is correct?

Accepted Answer

The work done by a conservative force is independent of the path taken.

Question 6

A spring with a constant $$k = 440\ \mathrm{N/m} is $$stretched to store $$25\ \mathrm{J} of $$energy. How far is it stretched?

Accepted Answer

$$x = \sqrt{\frac{2 	imes 25}{440}} \approx 0.337\ \mathrm{m}$$

Question 7

A 7 kg monkey swings from a branch 1.2 m above the ground. What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U = mgh = 7 	imes 9.8 	imes 1.2 = 82.32\ \mathrm{J}$$

Question 8

Which of the following is NOT a characteristic of non-conservative forces?

Accepted Answer

They do not change the total mechanical energy of a system.

Question 9

A 1200 kg car moving at $$65\ \mathrm{km/h}$$ hits a spring and comes to rest after compressing it by $$2.2\ \mathrm{m}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{mv^2$}{2x^2$}$$

Question 10

A skier starts from rest at the top of a frictionless incline of height $$185\ \mathrm{m}$$ and angle $$35^\circ. $$What is the skier's speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 185} \approx 60.3\ \mathrm{m/s}$$

Question 11

A roller coaster car is released from rest at a height of $$35\ \mathrm{m}. $$What is its speed at a height of $$15\ \mathrm{m}$$, neglecting friction?

Accepted Answer

$$v = \sqrt{2g(h_1$ - h_2$)} = \sqrt{2 	imes 9.8 	imes (35 - 15)} \approx 19.8\ \mathrm{m/s}$$

Question 12

A 1 kg mass is attached to a spring with $$k = 2000\ \mathrm{N/m}$$ and compressed $$0.1\ \mathrm{m}. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 2000 	imes (0.1)^2$ = 10\ \mathrm{J}$$

Question 13

Which equation correctly expresses the total mechanical energy of a system?

Accepted Answer

$$E = K + U$$

Question 14

A ball of mass $$0.14\ \mathrm{kg}$$ moving at $$32\ \mathrm{m/s} is $$caught by a glove that moves $$0.25\ \mathrm{m}$$ backward. What is the average force exerted by the glove?

Accepted Answer

$$F = \frac{mv^2$}{2d} = \frac{0.14 	imes 32^2$}{2 	imes 0.25} = 286\ \mathrm{N}$$

Question 15

A person of mass $$60\ \mathrm{kg}$$ climbs a $$2.2\ \mathrm{m}$$ ladder while holding a $$2.1\ \mathrm{kg}$$ book. What is the total increase in gravitational potential energy?

Accepted Answer

$$\Delta U = (60 + 2.1) 	imes 9.8 	imes 2.2 = 1332.6\ \mathrm{J}$$

Question 16

Which of the following best explains why friction is a non-conservative force?

Accepted Answer

Friction converts mechanical energy into thermal energy, which cannot be fully recovered.

Question 17

A 65 kg acrobat jumps vertically from a trampoline with a speed of $$5.0\ \mathrm{m/s}$$ from a height of $$3.0\ \mathrm{m}. $$What is his speed when he lands back on the trampoline?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh} = \sqrt{5^2$ + 2 	imes 9.8 	imes 3} \approx 9.1\ \mathrm{m/s}$$

Study Guide: Mechanical Energy, Work-Energy Theorem, and Conservation Principles

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