Q: A 12 N horizontal force pushes a 4 kg box 3.5 m across a frictionless surface. What is the final speed of the box after the force is applied?

$$v = \sqrt{\frac{2 \times 12 \times 3.5}{4}}$$

Q: A student pushes a 10 kg crate across the floor at constant speed for 8 m. The coefficient of kinetic friction is 0.30. How much work does friction do?

$$W = -\mu_k m g d = -0.30 \times 10 \times 9.8 \times 8$$

Q: A 1500 kg car has $$3.0 \times 10^5$ J of kinetic energy. What is the car’s speed?

$$v = \sqrt{\frac{2 \times 3.0 \times 10^5$}{1500}}$$

Q: A motor lifts a 25 kg mass vertically at a constant speed of 0.75 m/s. What power must the motor supply?

$$P = m g v = 25 \times 9.8 \times 0.75$$

Q: A 0.25 kg ball is released from rest at a height of 2.5 m. What is its speed just before it hits the ground, assuming conservation of mechanical energy?

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 2.5}$$

Q: A 0.50 kg aluminum block (specific heat $$c=900 J/(kg$$°C)) is heated from 20 °C to 75 °C. How much heat is absorbed by the block?

$$Q = m c \Delta T = 0.50 \times 900 \times (75 - 20)$$

Q: How much heat is required to melt 0.25 kg of ice at 0 °C into liquid water at 0 °C? (Latent heat of fusion $$L_f = 3.34 \times 10^5$ J/kg)

$$Q = m L_f = 0.25 \times 3.34 \times 10^5$

Q: A 2.0 cm-thick glass window (thermal conductivity $$k=1.0 W/(m$$\cdotpK)) has an area of 1 m². The inside surface is at 20 °C and the outside at –10 °C. What is the rate of heat conduction through the window?

$$Q = \frac{k A \Delta T}{d} = \frac{1.0 \times 1 \times (20 - (-10))}{0.02}$$

Q: A steel rod is 2.00 m long at 20 °C. The coefficient of linear expansion for steel is $$\alpha=1.2 \times 10$$^{-5}$$ °C$$^{-1}$$. How much longer is the rod at 80 °C?

$$\Delta L = L_0$ \alpha \Delta T = 2.00 \times 1.2 \times 10$$^{-5}$$ \times (80 - 20)$$

Question 1

A 12 N horizontal force pushes a 4 kg box 3.5 m across a frictionless surface. What is the final speed of the box after the force is applied?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 12 	imes 3.5}{4}}$$

Question 2

A student pushes a 10 kg crate across the floor at constant speed for 8 m. The coefficient of kinetic friction is 0.30. How much work does friction do?

Accepted Answer

$$W = -\mu_k m g d = -0.30 	imes 10 	imes 9.8 	imes 8$$

Question 3

A 1500 kg car has $$3.0 	imes 10^5$ J of kinetic energy. What is the car’s speed?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 3.0 	imes 10^5$}{1500}}$$

Question 4

A motor lifts a 25 kg mass vertically at a constant speed of 0.75 m/s. What power must the motor supply?

Accepted Answer

$$P = m g v = 25 	imes 9.8 	imes 0.75$$

Question 5

A 0.25 kg ball is released from rest at a height of 2.5 m. What is its speed just before it hits the ground, assuming conservation of mechanical energy?

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 2.5}$$

Question 6

A small appliance uses energy at a rate of 85 W. How much energy does it consume in 10 minutes?

Accepted Answer

$$E = P t = 85 	imes 600$$

Question 7

A metal rod has a temperature of 86 °F. What is this temperature in Celsius?

Accepted Answer

$$T_C = \frac{5}{9}(86 - 32)$$

Question 8

A 0.50 kg aluminum block (specific heat $$c=900 J/(kg$$°C)) is heated from 20 °C to 75 °C. How much heat is absorbed by the block?

Accepted Answer

$$Q = m c \Delta T = 0.50 	imes 900 	imes (75 - 20)$$

Question 9

A student mixes 200 g of water at 80 °C with 300 g of water at 20 °C in an insulated container. What is the final equilibrium temperature?

Accepted Answer

$$T_f = \frac{m_1$ T_1$ + m_2$ T_2$}{m_1$ + m_2$} = \frac{200 	imes 80 + 300 	imes 20}{200 + 300}$$

Question 10

How much heat is required to melt 0.25 kg of ice at 0 °C into liquid water at 0 °C? (Latent heat of fusion $$L_f = 3.34 	imes 10^5$ J/kg)

Accepted Answer

$$Q = m L_f = 0.25 	imes 3.34 	imes 10^5$

Question 11

A 2.0 cm-thick glass window (thermal conductivity $$k=1.0 W/(m$$\cdotpK)) has an area of 1 m². The inside surface is at 20 °C and the outside at –10 °C. What is the rate of heat conduction through the window?

Accepted Answer

$$Q = \frac{k A \Delta T}{d} = \frac{1.0 	imes 1 	imes (20 - (-10))}{0.02}$$

Question 12

A steel rod is 2.00 m long at 20 °C. The coefficient of linear expansion for steel is $$\alpha=1.2 	imes 10$$^{-5}$$ °C$$^{-1}$$. How much longer is the rod at 80 °C?

Accepted Answer

$$\Delta L = L_0$ \alpha \Delta T = 2.00 	imes 1.2 	imes 10$$^{-5}$$ 	imes (80 - 20)$$

Question 13

A small object has a charge of $$-4.8 	imes 10$$^{-19}$$ C. How many excess electrons does it have?

Accepted Answer

$$n = \frac{|q|}{e} = \frac{4.8 	imes 10$$^{-19}$$}{1.6 	imes 10$$^{-19}$$}$$

Question 14

Two charges, $$+2.0$$ μC and $$+3.0$$ μC, are 0.15 m apart. What is the magnitude of the electrostatic force between them?

Accepted Answer

$$F = \frac{k q_1$ q_2$}{r^2$} = \frac{8.99 	imes 10^9$ 	imes 2.0 	imes 10$$^{-6}$$ 	imes 3.0 	imes 10$$^{-6}$$}{(0.15)^2$}$$

Question 15

An electric field of magnitude $$E=2.5 	imes 10^5$ N/C points to the right. A charge of -3.0$ nC is placed in the field. What are the magnitude and direction of the force on the charge?

Accepted Answer

$$F = |q| E = 3.0 	imes 10$$^{-9}$$ 	imes 2.5 	imes 10^5$, \,	ext{to the left}$

Question 16

A 12 V battery is connected to a resistor of 4.0 Ω. What current flows through the resistor?

Accepted Answer

$$I = \frac{V}{R} = \frac{12}{4.0}$$

Question 17

A copper wire (resistivity $$1.68 	imes 10$$^{-8}$$ Ω⋅m) is 5.0 m long and has a cross-sectional area of 2.0$$ 	imes $$10^{-6} m$$². What is the resistance of the wire?

Accepted Answer

$$R = \frac{ho L}{A} = \frac{1.68 	imes 10$$^{-8}$$ 	imes 5.0}{2.0 	imes 10$$^{-6}$$}$$

Physics Study Guide: Work, Energy, Power, Thermal Physics, Electrostatics, and Circuits

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