Q: A 2 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14\ \mathrm{m/s}$$

Q: Katie starts at the top of a 9.0 m high frictionless water slide with an initial speed of 2.0 m/s. What is her speed at the bottom? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{v_0$^2 + 2gh} = \sqrt{2.0^2$ + 2 \times 9.8 \times 9.0} = \sqrt{4 + 176.4} = \sqrt{180.4} \approx 13.4\ \mathrm{m/s}$$

Q: A ball is thrown vertically upward with an initial speed of 20 m/s. Ignoring air resistance, what is the maximum height reached? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 \times 9.8} = \frac{400}{19.6} \approx 20.4\ \mathrm{m}$$

Q: A 5 kg object is moving at 10 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 5 \times 10^2$ = 250\ \mathrm{J}$$

Question 1

Which of the following best describes the Law of Conservation of Energy?

Accepted Answer

The total energy of an isolated system remains constant, though energy may change forms.

Question 2

A 2 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14\ \mathrm{m/s}$$

Question 3

Katie starts at the top of a 9.0 m high frictionless water slide with an initial speed of 2.0 m/s. What is her speed at the bottom? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh} = \sqrt{2.0^2$ + 2 	imes 9.8 	imes 9.0} = \sqrt{4 + 176.4} = \sqrt{180.4} \approx 13.4\ \mathrm{m/s}$$

Question 4

A 1000 kg car and an 85 kg bicycle (with rider) are released from rest at the top of a 100 m frictionless hill. Which will reach the bottom first and why?

Accepted Answer

Both reach the bottom at the same time because mass cancels out in the energy equations.

Question 5

Which equation correctly expresses the work-energy theorem for a system where work $$W is $$done on the system?

Accepted Answer

$$E_{f} = E_{i} + W$$

Question 6

Monica pulls a 25 kg trailer up a 100 m long slope that rises 4.0 m. The trailer starts at 5.3 m/s and Monica applies a constant force of 8.0 N parallel to the slope. What is the trailer's speed at the top? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{v_0$^2 + \frac{2Fd - 2mgh}{m}} = \sqrt{5.3^2$ + \frac{2 	imes 8.0 	imes 100 - 2 	imes 25 	imes 9.8 	imes 4.0}{25}} \approx 3.7\ \mathrm{m/s}$$

Question 7

In which scenario is the mass of an object NOT required to determine its final velocity using conservation of energy?

Accepted Answer

An object sliding down a frictionless hill with no external work done.

Question 8

Which of the following is the correct expression for gravitational potential energy?

Accepted Answer

$$U = mgh$$

Question 9

A ball is thrown vertically upward with an initial speed of 20 m/s. Ignoring air resistance, what is the maximum height reached? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 	imes 9.8} = \frac{400}{19.6} \approx 20.4\ \mathrm{m}$$

Question 10

Which of the following statements about mechanical energy in an isolated system is correct?

Accepted Answer

The sum of kinetic and potential energy remains constant if no work is done on the system.

Question 11

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

Accepted Answer

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

Question 12

A 5 kg object is moving at 10 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 5 	imes 10^2$ = 250\ \mathrm{J}$$

Question 13

If a system is not isolated and work is done on it, which of the following is true?

Accepted Answer

The total energy of the system changes by the amount of work done.

Question 14

A 10 kg box is lifted vertically by 2 m at constant speed. How much work is done against gravity? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$$

Question 15

Which of the following is NOT a form of mechanical energy?

Accepted Answer

Thermal energy

Question 16

A 3 kg object slides down a frictionless incline from a height of 5 m. What is its speed at the bottom? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = \sqrt{98} = 9.9\ \mathrm{m/s}$$

Question 17

Which of the following best explains why mass cancels out when calculating the final velocity of an object sliding down a frictionless hill?

Accepted Answer

Both kinetic and potential energy are proportional to mass, so mass divides out when equating energies.

Question 18

A 50 kg skier starts from rest at the top of a 20 m high hill. What is her speed at the bottom, assuming no friction? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} = \sqrt{392} = 19.8\ \mathrm{m/s}$$

Question 19

Which of the following is a correct application of the work-energy theorem in a real-world scenario?

Accepted Answer

A cyclist applies a force to pedal uphill, increasing both the kinetic and potential energy of the bike and rider.

Conservation of Energy and the Work-Energy Theorem

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