Q: A 2 kg object is dropped from a height of 5 m. Neglecting air resistance, what is its speed just before hitting the ground? (Use $$g = 9.80\ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.80 \times 5} = 9.9\ \text{m/s}$$

Q: A person climbs a staircase, raising their body by 2 m in 5 seconds. If their mass is 70 kg, what is the average power output? (Use $$g = 9.80\ \text{m/s}^2)$$

$$P = \frac{mgh}{t} = \frac{70 \times 9.80 \times 2}{5} = 274.4\ \text{W}$$

Q: A gas in a cylinder is compressed at constant temperature from 2 L to 1 L. If the initial pressure is 1 atm, what is the final pressure?

$$p_2$$ = \frac{$$p_1$$ $$V_1$$}{$$V_2$$} = \frac{1 \times 2}{1} = 2\ \text{atm}$$

Question 1

A spring with spring constant $$k is $$stretched by a distance $$x. If $$the stretch is doubled, by what factor does the elastic potential energy stored in the spring change?

Accepted Answer

It increases by a factor of 4.

Question 2

A 2 kg object is dropped from a height of 5 m. Neglecting air resistance, what is its speed just before hitting the ground? (Use $$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.80 	imes 5} = 9.9\ 	ext{m/s}$$

Question 3

Which of the following best describes the energy transformation when a car brakes to a stop?

Accepted Answer

Kinetic energy is converted to thermal energy.

Question 4

A person climbs a staircase, raising their body by 2 m in 5 seconds. If their mass is 70 kg, what is the average power output? (Use $$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$P = \frac{mgh}{t} = \frac{70 	imes 9.80 	imes 2}{5} = 274.4\ 	ext{W}$$

Question 5

A heat engine absorbs 500 J of heat from the hot reservoir and does 120 J of work. What is its efficiency?

Accepted Answer

$$e = \frac{W}{Q_H} = \frac{120}{500} = 0.24$$

Question 6

A refrigerator removes 200 J of heat from its interior and expels 250 J to the environment. What is its coefficient of performance (COP)?

Accepted Answer

$$COP = \frac{Q_C}{W} = \frac{200}{250 - 200} = 4$$

Question 7

A person consumes 1000 J of metabolic energy and performs 250 J of useful work. What is the efficiency of the human body in this scenario?

Accepted Answer

$$e = \frac{W}{E_{met}} = \frac{250}{1000} = 0.25$$

Question 8

Which statement about temperature is correct?

Accepted Answer

Temperature is a measure of the average kinetic energy of the particles in a substance.

Question 9

A 100 g piece of metal at 80°C is placed in 200 g of water at 20°C. If the final equilibrium temperature is 30°C, what is the specific heat of the metal? (Assume $$c_{water} = 4.18\ 	ext{J/g} \cdot 	ext{°C})$$

Accepted Answer

$$c_{metal} = \frac{m_{water} c_{water} (T_f - T_{water})}{m_{metal} (T_{metal} - T_f)} = \frac{200 	imes 4.18 	imes (30 - 20)}{100 	imes (80 - 30)} = 1.67\ 	ext{J/g} \cdot 	ext{°C}$$

Question 10

On a $$p$$-$$V$$ diagram, which process represents an isothermal expansion of an ideal gas?

Accepted Answer

A curve where $$pV$$ remains constant.

Question 11

A gas in a cylinder is compressed at constant temperature from 2 L to 1 L. If the initial pressure is 1 atm, what is the final pressure?

Accepted Answer

$$p_2$$ = \frac{$$p_1$$ $$V_1$$}{$$V_2$$} = \frac{1 	imes 2}{1} = 2\ 	ext{atm}$$

Question 12

A force of 500 N is applied over an area of 0.2 m². What is the pressure exerted?

Accepted Answer

$$P = \frac{F}{A} = \frac{500}{0.2} = 2500\ 	ext{Pa}$$

Question 13

Which material will experience the smallest temperature change when absorbing the same amount of heat?

Accepted Answer

A material with a large specific heat.

Question 14

If the mass attached to a spring is quadrupled, how does the period of oscillation change?

Accepted Answer

The period doubles. $$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 15

If the length of a pendulum is doubled, how does its period change?

Accepted Answer

The period increases by a factor of $$\sqrt{2}$$. $$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 16

A pendulum has a length of 1.5 m. What is its period? (Use $$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$T = 2\pi \sqrt{\frac{1.5}{9.80}} = 2\pi \sqrt{0.153} = 2\pi 	imes 0.391 = 2.46\ 	ext{s}$$

Question 17

A mass on a spring oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is its maximum velocity?

Accepted Answer

$$v_{max} = \omega A$$

Question 18

A 0.5 kg mass attached to a spring with $$k = 200\ 	ext{N/m}$$ oscillates. What is its maximum acceleration if the amplitude is 0.1 m?

Accepted Answer

$$a_{max} = \frac{k}{m} A = \frac{200}{0.5} 	imes 0.1 = 40\ 	ext{m/s}^2$$

PHYS 111 Exam #4 Review: Energy, Thermal Physics, and Oscillations

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