Question 1

A 0.150-kg baseball is thrown straight upward with an initial speed of 20.0 m/s. Ignoring air resistance, what is the maximum height reached by the ball? Use $g = 9.8\ \mathrm{m/s^2}$.

Accepted Answer

$20.4\ \mathrm{m}$

Question 2

Which of the following statements about conservative forces is TRUE?

Accepted Answer

A conservative force has a corresponding potential energy function.

Question 3

A block of mass $m$ slides down a frictionless ramp of height $h$ and then compresses a spring with force constant $k$. What is the maximum compression $x_{max}$ of the spring?

Accepted Answer

$x_{max} = \sqrt{\dfrac{2 m g h}{k}}$

Question 4

Which of the following is a property of nonconservative forces?

Accepted Answer

They convert mechanical energy into internal energy.

Question 5

A block is released from rest on a frictionless incline and compresses a spring at the bottom. While the block is compressing the spring, what happens to the gravitational potential energy $U_g$ and the elastic potential energy $U_s$?

Accepted Answer

$U_g$ is decreasing; $U_s$ is increasing.

Question 6

A 25.0-kg skateboarder starts from rest at the top of a frictionless quarter-circle ramp of radius $R = 3.00\ \mathrm{m}$. What is the speed at the bottom of the ramp?

Accepted Answer

$7.67\ \mathrm{m/s}$

Question 7

Which of the following best describes the law of conservation of energy?

Accepted Answer

Energy is never created or destroyed; it only changes form.

Question 8

A block slides on a frictionless surface under the influence of a conservative force with potential energy $U(x)$. At which point is the force on the block zero?

Accepted Answer

Where $\dfrac{dU}{dx} = 0$

Question 9

A force $F(x)$ acts on a particle such that $F(x) = -k x$. What is the corresponding potential energy function $U(x)$?

Accepted Answer

$U(x) = \dfrac{1}{2} k x^2$

Question 10

You push a block up an inclined ramp at constant speed. There is friction between the block and the ramp. The rate at which the internal energy of the block and ramp increases is:

Accepted Answer

The same as the rate at which you do work on the block.

Question 11

A particle moves along the x-axis under the influence of a potential energy function $U(x)$. At which point is the equilibrium stable?

Accepted Answer

Where $U(x)$ is at a minimum.

Question 12

A spring with force constant $k$ is compressed by a distance $x$. What is the elastic potential energy stored in the spring?

Accepted Answer

$U = \dfrac{1}{2} k x^2$

Question 13

A hiker climbs a mountain with steep slopes. What does a large gradient in gravitational potential energy $U_g$ indicate?

Accepted Answer

A strong force pushing the hiker toward lower elevation.

Question 14

Which of the following is TRUE about the work done by gravity when a fruit falls straight down?

Accepted Answer

Gravity does positive work and gravitational potential energy decreases.

Question 15

A block of mass $m$ is released from rest at height $h$ on two different frictionless ramps (one straight, one curved) of the same height. Which block arrives at the bottom with greater speed?

Accepted Answer

Both blocks arrive with the same speed.

Question 16

A particle moves along the x-axis under a potential energy function $U(x)$. At which point is the particle in unstable equilibrium?

Accepted Answer

Where $U(x)$ is at a maximum.

Question 17

A block slides on a frictionless surface under a conservative force $F(x)$. If $F(x) = 0$ at $x = a$, which statement about the potential energy $U(x)$ at $x = a$ is correct?

Accepted Answer

$\dfrac{dU}{dx} = 0$ at $x = a$.

Question 18

A block moves under a conservative force in two dimensions, with potential energy $U(x, y) = k \sqrt{x^2 + y^2}$. What is the magnitude of the force at position $(x, y)$?

Accepted Answer

$F = k / \sqrt{x^2 + y^2}$

Question 19

Which of the following is TRUE about the total mechanical energy of a system when only gravity does work?

Accepted Answer

It is conserved.

Potential Energy and Energy Conservation (Chapter 7 Study Notes)

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