Q: A 2 kg object is dropped from a height of 5 m. Neglecting air resistance, what is the object's speed just before it hits 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 1.5 m in 5 seconds. If their mass is 70 kg, what is the average power output during the climb? (Use $$g = 9.80\ \text{m/s}^2)$$

$$P = \frac{mgh}{t} = \frac{70 \times 9.80 \times 1.5}{5} = 206\ \text{W}$$

Q: A force of 200 N is applied over an area of $$0.02\ \text{m}^2. $$What is the pressure exerted?

$$P = \frac{F}{A} = \frac{200}{0.02} = 10,000\ \text{Pa}$$

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 the object's speed just before it hits 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

A person climbs a staircase, raising their body by 1.5 m in 5 seconds. If their mass is 70 kg, what is the average power output during the climb? (Use $$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$P = \frac{mgh}{t} = \frac{70 	imes 9.80 	imes 1.5}{5} = 206\ 	ext{W}$$

Question 4

A heat engine absorbs 500 J of heat from a hot reservoir and expels 300 J to a cold reservoir. What is the efficiency of the engine?

Accepted Answer

$$\eta = \frac{W}{Q_H} = \frac{500 - 300}{500} = 0.4$$

Question 5

A refrigerator removes 1200 J of heat from its interior and requires 400 J of work. What is its coefficient of performance (COP)?

Accepted Answer

$$COP = \frac{Q_C}{W} = \frac{1200}{400} = 3$$

Question 6

A 60 kg runner expends 3000 J of metabolic energy to do 600 J of mechanical work. What is the efficiency of the runner's body?

Accepted Answer

$$\eta = \frac{W}{E_{met}} = \frac{600}{3000} = 0.2$$

Question 7

Which of the following best describes the difference between temperature and heat?

Accepted Answer

Temperature is a measure of the average kinetic energy of particles, while heat is energy transferred due to temperature difference.

Question 8

A 0.5 kg block at 80°C is placed in 1 kg of water at 20°C. If the final equilibrium temperature is 25°C, what is the specific heat of the block? (Assume $$c_{water} = 4186\ 	ext{J/kg} \cdot 	ext{K})$$

Accepted Answer

$$c_{block} = \frac{m_{water} c_{water} (T_f - T_{water})}{m_{block} (T_{block} - T_f)} = \frac{1 	imes 4186 	imes (25 - 20)}{0.5 	imes (80 - 25)} = 761\ 	ext{J/kg} \cdot 	ext{K}$$

Question 9

A gas undergoes an isothermal expansion from 2 L to 6 L at a constant temperature. Which process is this on a $$p$$-$$V$$ diagram?

Accepted Answer

A curve that decreases as volume increases, representing $$pV = 	ext{constant}$$

Question 10

A force of 200 N is applied over an area of $$0.02\ 	ext{m}^2. $$What is the pressure exerted?

Accepted Answer

$$P = \frac{F}{A} = \frac{200}{0.02} = 10,000\ 	ext{Pa}$$

Question 11

Which material will experience the smallest temperature change when absorbing the same amount of heat: water ($$c = 4186\ 	ext{J/kg} \cdot 	ext{K}$$), iron ($$c = 450\ 	ext{J/kg} \cdot 	ext{K}$$), or copper ($$c = 385\ 	ext{J/kg} \cdot 	ext{K}$$)?

Accepted Answer

Water, because it has the largest specific heat.

Question 12

A mass $$m is $$attached to a spring with spring constant $$k. If $$the mass is quadrupled, how does the period of oscillation change?

Accepted Answer

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

Question 13

A pendulum has a length of 1 m. What is its period on Earth? (Use $$g = 9.80\ 	ext{m/s}^2)$$

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{1}{9.80}} = 2.01\ 	ext{s}$$

Question 14

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

Accepted Answer

The period increases by a factor of $$\sqrt{2}.$$

Question 15

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 16

A 3 kg object is acted upon by a force of 15 N over a distance of 4 m. What is the work done on the object?

Accepted Answer

$$W = F \cdot d = 15 	imes 4 = 60\ 	ext{J}$$

Question 17

A car engine does 2000 J of work and wastes 3000 J as heat. What is the efficiency of the engine?

Accepted Answer

$$\eta = \frac{W}{W + Q_{wasted}} = \frac{2000}{2000 + 3000} = 0.4$$

Question 18

A 0.2 kg mass oscillates on a spring with $$k = 50\ 	ext{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{0.2}{50}} = 0.4\ 	ext{s}$$

Question 19

A 1 kg block at 100°C is placed in 2 kg of water at 20°C. If the final temperature is 30°C, what is the heat lost by the block? (Assume $$c_{block} = 500\ 	ext{J/kg} \cdot 	ext{K})$$

Accepted Answer

$$Q = m c \Delta T = 1 	imes 500 	imes (100 - 30) = 35,000\ 	ext{J}$$

PHYS 111 Exam #4 Review: Energy, Thermodynamics, and Oscillations

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