Q: Your Achilles tendon stretches by $$0.0050\ \mathrm{m}$$ when you run, and the spring constant is $$1.67 \times 10^5$\ \mathrm{N/m}. $$How much energy is stored for this stretch?

$$U = \frac{1}{2} (1.67 \times 10^5$)(0.0050)^2 = 2.1$$\ \mathrm{J}$

Question 1

Which of the following statements best describes a conservative force?

Accepted Answer

A force that can store useful energy and convert it to other forms, such as gravity or elastic forces.

Question 2

A ball of mass $$m is $$lifted to a height $$h$$ above the ground. What is its gravitational potential energy relative to the ground?

Accepted Answer

$$U_g = mgh$$

Question 3

Rank the gravitational potential energies of four balls, where ball 3 is at ground level ($$y=0$$), ball 2 is above ball 3, ball 4 is above ball 2, and ball 1 is above ball 4. Which is the correct order from largest to smallest?

Accepted Answer

3 \u003c 2 \u003c 4 \u003c 1

Question 4

A marble rolls down two hills of the same height, one steeper than the other. Neglecting friction, how does its speed at the bottom compare?

Accepted Answer

Same speed at the bottom of both hills.

Question 5

A child slides down four frictionless slides of different shapes but the same height. Rank her speeds at the bottom from largest to smallest.

Accepted Answer

$$v_A = v_B = v_C = v_D$$

Question 6

Three balls are thrown from a cliff with the same speed but at different angles. Which ball has the greatest speed just before it hits the ground?

Accepted Answer

All balls have the same speed.

Question 7

A hockey puck slides on smooth ice at $$4\ \mathrm{m/s}$$ and comes to a $$1\ \mathrm{m}$$ high hill. Will it make it to the top of the hill?

Accepted Answer

No.

Question 8

What is the formula for the elastic potential energy stored in a spring displaced a distance $$x$$ from equilibrium?

Accepted Answer

$$U_e = \frac{1}{2}kx^2$

Question 9

Your Achilles tendon stretches by $$0.0050\ \mathrm{m}$$ when you run, and the spring constant is $$1.67 	imes 10^5$\ \mathrm{N/m}. $$How much energy is stored for this stretch?

Accepted Answer

$$U = \frac{1}{2} (1.67 	imes 10^5$)(0.0050)^2 = 2.1$$\ \mathrm{J}$

Question 10

Thermal energy is best described as:

Accepted Answer

The sum of the kinetic energy of atoms and molecules and the elastic potential energy stored in molecular bonds.

Question 11

Friction on a moving object does work and creates thermal energy. Which equation best represents the change in thermal energy due to friction?

Accepted Answer

$$\Delta E_{th} = f_s \Delta x$$

Question 12

Which equation expresses the law of conservation of energy for an isolated system?

Accepted Answer

$$K_i + U_i + \Delta E_{th} = K_f + U_f$$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

A car of mass $$m$$ starts at rest at the top of a hill of height $$h. $$After rolling down, what is its speed at the bottom, assuming no friction?

Accepted Answer

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

Question 16

A child slides down a slide at constant speed. The height of the slide is $$3.0\ \mathrm{m}. $$What energy transformation occurs?

Accepted Answer

Gravitational potential energy is converted into thermal energy.

Question 17

Quinn slides down a $$5.0\ \mathrm{m}$$ long slide at a $$30^\circ$$ angle, leaving the slide at $$2.0\ \mathrm{m/s}. If $$Quinn's mass is $$24\ \mathrm{kg}$$, how much thermal energy is deposited in his trousers and the slide?

Accepted Answer

$$540\ \mathrm{J}$$

Question 18

Which of the following is NOT a form of potential energy discussed in the lecture?

Accepted Answer

Thermal energy

Potential Energy, Thermal Energy, and Conservation of Energy

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