Q: A 60 kg skier starts from rest at the top of an 85 m long hill inclined at $$28^\circ. $$The coefficient of kinetic friction between the skis and the snow is 0.090. What is the skier's speed at the bottom of the hill?

$$v = \sqrt{2gL(\sin\theta - \mu_k \cos\theta)}$$

Q: A person runs at 15 km/hr with a metabolic power output of 1150 W for 30 minutes. How much energy (in kilojoules) do they use?

$$E = 1150 \times 1800 / 1000 = 2070\ \mathrm{kJ}$$

Q: A typical person radiates energy at a rate of 186 W. How long (in hours) would it take to radiate away the energy used during the 30-minute run (2070 kJ)?

$$t = \frac{2070 \times 1000}{186 \times 3600} \approx 3.1\ \mathrm{hours}$$

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

$$KE = mgh = 2 \times 9.8 \times 10 = 196\ \mathrm{J}$$

Q: A spring with a spring constant $$k = 500\ \mathrm{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} \times 500 \times (0.1)^2$ = 2.5\ \mathrm{J}$$

Question 1

A 60 kg skier starts from rest at the top of an 85 m long hill inclined at $$28^\circ. $$The coefficient of kinetic friction between the skis and the snow is 0.090. What is the skier's speed at the bottom of the hill?

Accepted Answer

$$v = \sqrt{2gL(\sin	heta - \mu_k \cos	heta)}$$

Question 2

A 60 kg skier reaches the bottom of the hill described above. If the snow is level at the bottom and the coefficient of friction remains 0.090, how far will the skier travel before coming to rest?

Accepted Answer

$$d = \frac{v^2$}{2\mu_k g}$$

Question 3

A person runs at 15 km/hr with a metabolic power output of 1150 W for 30 minutes. How much energy (in kilojoules) do they use?

Accepted Answer

$$E = 1150 	imes 1800 / 1000 = 2070\ \mathrm{kJ}$$

Question 4

If a carrot contains 125 kJ of energy, how many carrots must the runner from the previous question eat to replenish the energy used?

Accepted Answer

$$n = \frac{2070}{125} = 16.56 \approx 17$$

Question 5

A typical person radiates energy at a rate of 186 W. How long (in hours) would it take to radiate away the energy used during the 30-minute run (2070 kJ)?

Accepted Answer

$$t = \frac{2070 	imes 1000}{186 	imes 3600} \approx 3.1\ \mathrm{hours}$$

Question 6

Which of the following best describes the First Law of Thermodynamics?

Accepted Answer

Energy cannot be created or destroyed, only transformed from one form to another.

Question 7

Which of the following statements about entropy is correct?

Accepted Answer

Entropy is a measure of the disorder or randomness of a system.

Question 8

A 1600 ft$$^2$$ house (40 ft x 40 ft, 10 ft high walls, wall thickness 6.5 in, thermal conductivity $$k = 0.17\ \mathrm{W/(m\ K)}) is $$kept at $$70^\circF $$while it is $$0^\circF $$outside. What is the rate of heat conduction through the four exterior walls?

Accepted Answer

$$Q/t = \frac{kA\Delta T}{d}$$

Question 9

If the roof of the house has an emissivity of 0.92 and is flat, what is the rate of heat transfer by radiation through the roof? (Assume $$T_{in}$$ and $$T_{out}$$ are in Kelvin.)

Accepted Answer

$$P = \varepsilon \sigma A (T_{in}^4 - T_{out}^4)$$

Question 10

Which of the following is NOT a correct statement about energy transformations in the human body?

Accepted Answer

All chemical energy from food is converted into mechanical work.

Question 11

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

Accepted Answer

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

Question 12

A spring with a spring constant $$k = 500\ \mathrm{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 500 	imes (0.1)^2$ = 2.5\ \mathrm{J}$$

Question 13

Which of the following best describes the Second Law of Thermodynamics?

Accepted Answer

The entropy of an isolated system never decreases; it increases for irreversible processes.

Question 14

A 0.5 kg block of aluminum ($$c = 900\ \mathrm{J/(kg\cdot K)}) at$$ $$100^\circC is $$placed in 1 kg of water ($$c = 4186\ \mathrm{J/(kg\cdot K)}) at$$ $$20^\circC. $$What is the final equilibrium temperature? (Neglect heat loss to the environment.)

Accepted Answer

$$m_{Al}c$$_{Al}(T_f - 100) + $$m_{H_2O}c$$_{H_2O}(T_f - 20) = 0$$

Question 15

Which of the following is the correct formula for the rate of heat transfer by conduction through a wall?

Accepted Answer

$$Q/t = \frac{kA\Delta T}{d}$$

Question 16

A 0.2 m$$^2$$ window is made of glass 0.005 m thick with thermal conductivity $$k = 0.8\ \mathrm{W/(m\cdot K)}. If $$the temperature difference across the window is $$20^\circC$$, what is the rate of heat transfer through the window?

Accepted Answer

$$Q/t = \frac{0.8 	imes 0.2 	imes 20}{0.005} = 640\ \mathrm{W}$$

Question 17

Which of the following is the correct formula for the efficiency of a heat engine?

Accepted Answer

$$e = 1 - \frac{Q_C}{Q_H}$$

Question 18

Which of the following is a correct statement about energy diagrams?

Accepted Answer

They show how potential energy changes with position and can be used to analyze motion and stability.

Physics Study Guide: Energy, Work, Power, and Thermodynamics

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