Q: What is the work done to stretch a spring with $$k = 30\ \mathrm{N/m}$$ from its equilibrium position to $$x = 0.10\ \mathrm{m}$$?

$$W = 0.5\times 30\times (0.10)^2$ = 0.15\ \mathrm{J}$$

Q: A 1.5 kg mass hangs from a spring and stretches it by $$\Delta L = 0.12\ \mathrm{m}. $$What is the spring constant $$k$$?

$$k = \frac{mg}{\Delta L} = \frac{1.5\times 9.8}{0.12} = 122.5\ \mathrm{N/m}$$

Q: A $$2.0\ \mathrm{kg}$$ object is dropped from a height of $$5.0\ \mathrm{m}. $$What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2\times 9.8\times 5.0} = 9.9\ \mathrm{m/s}$$

Q: A roller coaster passes point 1 with speed $$v_1 = 1.70$$\ \mathrm{m/s}$$ and travels 45.0$$\ \mathrm{m}$$ to point 2. If the average friction force is $$\frac{1}{5}$$ of its weight, what is the work done by friction?

$$W_{fric} = -\frac{1}{5}mg \times 45.0$$

Question 1

A spring with a spring constant $$k = 50\ \mathrm{N/m} is $$stretched by $$x = 0.20\ \mathrm{m}. $$What is the magnitude of the force exerted by the spring according to Hooke's Law?

Accepted Answer

$$F = 10\ \mathrm{N}$$

Question 2

What is the work done to stretch a spring with $$k = 30\ \mathrm{N/m}$$ from its equilibrium position to $$x = 0.10\ \mathrm{m}$$?

Accepted Answer

$$W = 0.5	imes 30	imes (0.10)^2$ = 0.15\ \mathrm{J}$$

Question 3

A 1.5 kg mass hangs from a spring and stretches it by $$\Delta L = 0.12\ \mathrm{m}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{mg}{\Delta L} = \frac{1.5	imes 9.8}{0.12} = 122.5\ \mathrm{N/m}$$

Question 4

Which of the following statements about gravitational potential energy is correct?

Accepted Answer

It increases as the object moves upward.

Question 5

A $$2.0\ \mathrm{kg}$$ object is dropped from a height of $$5.0\ \mathrm{m}. $$What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2	imes 9.8	imes 5.0} = 9.9\ \mathrm{m/s}$$

Question 6

A roller coaster car of mass $$m$$ starts from rest at height $$h$$ and descends to a lower height $$h/2$$ with no friction. What is its speed at the lower height?

Accepted Answer

$$v = \sqrt{2g(h - h/2)} = \sqrt{gh}$$

Question 7

Which of the following is true for a conservative force?

Accepted Answer

The work done is independent of the path taken.

Question 8

A ball is thrown horizontally, straight up, and straight down from the same height with the same speed. Which ball has the greatest speed just before hitting the ground (ignore air resistance)?

Accepted Answer

All balls have the same speed.

Question 9

The force associated with a potential energy function $$U(x) in $$one dimension is given by:

Accepted Answer

$$F_x(x) = -\frac{dU}{dx}$$

Question 10

A glider attached to a spring oscillates on a frictionless air track. If the total mechanical energy is $$E$$, what is the maximum displacement from equilibrium?

Accepted Answer

$$A = \sqrt{\frac{2E}{k}}$$

Question 11

A roller coaster passes point 1 with speed $$v_1$$ and height $$h_1$$, and point 2 with height $$h_2. If $$friction is negligible, what is its speed at point 2?

Accepted Answer

$$v_2$$ = \sqrt{$$v_1^2 + 2g$$($$h_1$$ - $$h_2$$)}$$

Question 12

Which of the following is NOT a property of a conservative force?

Accepted Answer

The work done depends on the path taken.

Question 13

A car tire heats up after driving due to nonconservative forces. What happens to the mechanical energy lost?

Accepted Answer

It is converted into internal energy (heat) of the tire.

Question 14

A mass $$m is $$attached to a spring and oscillates with amplitude $$A. $$What is the maximum kinetic energy during the motion?

Accepted Answer

$$K_{max} = \frac{1}{2}kA^2$

Question 15

A particle moves in a potential $$U(x)$$ with a minimum at $$x_0. $$What type of equilibrium is at $$x_0$$?

Accepted Answer

Stable equilibrium

Question 16

A marble rolls down two different tracks from the same height. Track A is straight, Track B is curved and dips below the straight line before rising to the same final height. Which marble reaches the end first (ignore friction)?

Accepted Answer

The marble on Track B

Question 17

A roller coaster passes point 1 with speed $$v_1 = 1.70$$\ \mathrm{m/s}$$ and travels 45.0$$\ \mathrm{m}$$ to point 2. If the average friction force is $$\frac{1}{5}$$ of its weight, what is the work done by friction?

Accepted Answer

$$W_{fric} = -\frac{1}{5}mg 	imes 45.0$$

Question 18

The force in three dimensions from a potential energy function $$U(x, y, z) is $$given by:

Accepted Answer

$$\vec{F} = -\left( \frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j} + \frac{\partial U}{\partial z} \hat{k} \right)$$

Potential Energy, Work, and Conservation of Energy: Study Notes for Physics with Calculus

Study Guide - Practice Questions

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