Q: A block is released from rest on a frictionless incline and compresses a spring at the bottom. As the block compresses the spring, what happens to the gravitational potential energy $$U_{\text{grav}}$$ and the elastic potential energy $$U_{\text{el}}$$?

$$U_{\text{grav}} is $$decreasing; $$U_{\text{el}} is $$increasing.

Question 1

A bungee jumper leaps from a bridge with a bungee cord attached to her ankles. As she falls and the cord stretches, which of the following best describes the energy transformations taking place?

Accepted Answer

Gravitational potential energy is converted to kinetic energy, and then to elastic potential energy as the cord stretches.

Question 2

A skier starts at the top of a hill and can choose between four different runs (a, b, c, d), all ending at the same elevation. Neglecting friction, on which run will the skier have the greatest speed at the bottom?

Accepted Answer

The skier will have the same speed at the bottom for all runs.

Question 3

A 0.145 kg baseball is thrown upward with a speed of 20.0 m/s. What is the maximum height it reaches? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$20.4\ \mathrm{m}$$

Question 4

A block of mass $$m$$ slides down a frictionless curved ramp from height $$y_1 to$$ $$y_2. $$What is the work done by gravity?

Accepted Answer

$$mg(y_1$ - y_2$)$$

Question 5

A rock of mass $$m is $$dropped from a height $$h. A $$second rock, with mass $$2m$$, is dropped from the same height. When the second rock strikes the ground, its kinetic energy is:

Accepted Answer

Twice that of the first rock.

Question 6

A pendulum of length $$L is $$released from rest at an angle $$	heta_A$$ with the vertical. What is the speed of the mass at the lowest point?

Accepted Answer

$$\sqrt{2gL(1-\cos	heta_A)}$$

Question 7

A block is released from rest on a frictionless incline and compresses a spring at the bottom. As the block compresses the spring, what happens to the gravitational potential energy $$U_{	ext{grav}}$$ and the elastic potential energy $$U_{	ext{el}}$$?

Accepted Answer

$$U_{	ext{grav}} is $$decreasing; $$U_{	ext{el}} is $$increasing.

Question 8

Which of the following is a property of a conservative force?

Accepted Answer

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

Question 9

A ball is dropped from a height $$h$$ and falls freely under gravity. What is its speed when it has fallen to a height $$y$$ above the ground?

Accepted Answer

$$\sqrt{2g(h-y)}$$

Question 10

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and is pulled a distance $$x$$ from equilibrium and released from rest. What is the maximum speed of the block?

Accepted Answer

$$x\sqrt{\frac{k}{m}}$$

Question 11

A particle moves along the x-axis in a potential $$U(x). At $$which point is the force on the particle zero?

Accepted Answer

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

Question 12

A block slides down a frictionless track from height $$y_1 to$$ $$y_2. If $$the block starts from rest, what is its speed at $$y_2$$?

Accepted Answer

$$\sqrt{2g(y_1$-y_2$)}$$

Question 13

A 25.0 kg skateboarder starts from rest at the top of a frictionless quarter-circle ramp of radius 3.00 m. What is his speed at the bottom?

Accepted Answer

$$7.67\ \mathrm{m/s}$$

Question 14

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

Accepted Answer

It is a shared property of the body and the Earth.

Question 15

A tomato is thrown upward. As it rises, what happens to its kinetic and gravitational potential energy?

Accepted Answer

Kinetic energy decreases, gravitational potential energy increases.

Question 16

A particle moves in a potential $$U(x). At a $$point where $$U(x) is at a $$minimum, what type of equilibrium does the particle have?

Accepted Answer

Stable equilibrium

Question 17

If only conservative forces act on a system, which of the following is true?

Accepted Answer

The total mechanical energy of the system is conserved.

Question 18

A block is lifted vertically upward at constant speed by a person. Which statement is correct about the work done and the change in gravitational potential energy?

Accepted Answer

The person does positive work, and the gravitational potential energy increases.

Question 19

A ball is thrown horizontally from the top of a building, while another is thrown at an angle, and a third is thrown straight down, all with the same initial speed. Neglecting air resistance, which ball has the greatest speed when it hits the ground?

Accepted Answer

All three balls have the same speed when they hit the ground.

Potential Energy and Energy Conservation: Gravitational and Mechanical Energy

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