Q: A 0.5 kg ball is dropped from a height of 10 m above the ground. Neglecting air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ \text{m/s}^2)$$

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

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

$$U_{\text{sp}} = \frac{1}{2} k \Delta s^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A skier glides down a gentle slope at constant speed. Which energy transformation is taking place?

$$U_G \rightarrow E_{\text{th}}$$

Question 1

A 0.5 kg ball is dropped from a height of 10 m above the ground. Neglecting air resistance, what is the speed of the ball just before it hits the ground? (Take $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

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

Question 2

Which of the following statements about potential energy is correct?

Accepted Answer

Potential energy is stored inside a system via interaction forces and is associated only with conservative forces.

Question 3

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

Accepted Answer

$$U_{	ext{sp}} = \frac{1}{2} k \Delta s^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 4

A skier glides down a gentle slope at constant speed. Which energy transformation is taking place?

Accepted Answer

$$U_G ightarrow E_{	ext{th}}$$

Question 5

A pendulum is released from rest at a height $$h$$ above its lowest point. What is its speed at the lowest point?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 6

Which equation correctly relates the change in potential energy $$\Delta U to $$the work done by a conservative force $$W$$?

Accepted Answer

$$\Delta U = -W$$

Question 7

A spring-loaded gun shoots a ball with a launch speed of $$2.0\ 	ext{m/s}. If $$the spring is compressed twice as far, what is the new launch speed?

Accepted Answer

$$4.0\ 	ext{m/s}$$

Question 8

A block of mass $$m is $$placed on a vertical spring of spring constant $$k. $$What is the equilibrium compression of the spring?

Accepted Answer

$$\Delta y = \frac{mg}{k}$$

Question 9

Which of the following is true about the work done by a conservative force?

Accepted Answer

It is independent of the path taken between two points.

Question 10

A hockey puck slides on smooth ice at $$4\ 	ext{m/s}$$ and comes to a $$1\ 	ext{m}$$ high hill. Will it make it to the top? (Neglect friction and air resistance.)

Accepted Answer

Yes.

Question 11

For a conservative force, the force at position $$s is $$given by:

Accepted Answer

$$F = -\frac{dU}{ds}$$

Question 12

A child slides down four frictionless slides of different shapes but the same vertical height. Rank her speeds at the bottom.

Accepted Answer

Her speed is the same at the bottom of all slides.

Question 13

Which of the following is NOT a property of mechanical energy in an isolated, nondissipative system?

Accepted Answer

Mechanical energy includes thermal energy.

Question 14

A mountain climber drags a bag of supplies up a slope at constant speed. Which energy transformation occurs?

Accepted Answer

Work by tension increases both gravitational potential energy and thermal energy.

Question 15

A particle moves in a region where its potential energy increases with position. What happens to its speed?

Accepted Answer

It slows down.

Question 16

Which of the following is true about the zero of potential energy?

Accepted Answer

Only the change in potential energy $$\Delta U$$ has physical significance.

Question 17

A spring-loaded gun shoots a ball with a launch speed of $$2.0\ 	ext{m/s}. If $$the spring is replaced with a new spring having twice the spring constant (but compressed the same distance), what is the new launch speed?

Accepted Answer

$$2.8\ 	ext{m/s}$$

Question 18

Which of the following is a nonconservative force?

Accepted Answer

Friction

Question 19

A particle is released from rest at position $$x_1 on a $$potential energy curve. Its total energy equals its potential energy at $$x_1. $$What happens as it moves?

Accepted Answer

It speeds up as potential energy decreases.

Question 20

Which of the following best describes stable equilibrium in an energy diagram?

Accepted Answer

A minimum in the potential energy curve where small disturbances cause small oscillations.

Chapter 10: Interactions and Potential Energy – Study Notes

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