Q: A 70.0 kg running back is moving north at 5.00 m/s and collides with an 80.0 kg linebacker moving west at 4.00 m/s. After they grab onto each other, what is the magnitude of their combined velocity immediately after the collision?

$$\sqrt{\left(\frac{70.0 \times 5.00}{150.0}\$$right)^2$$ + \left(\frac{80.0 \times 4.00}{150.0}\$$right)^2$$} = 2.67 m/s$$

Q: A 4.00 kg bomb at rest explodes into three pieces. Piece 1 (1.00 kg) flies north at 20.0 m/s, and Piece 2 (1.50 kg) flies east at 16.0 m/s. What is the magnitude of the velocity of Piece 3 immediately after the explosion?

$$\sqrt{(1.00 \times 20.0)^2$ + (1.50 \times 16.0)^2$} / 1.50 = 18.7 m/s$$

Q: A piston compresses 0.500 mol of ideal gas from $$V_1 = 10.0$ L to V_2$ = 2.50 L at $$constant $$T = 350 K. $$What is the work done on the gas during this compression?

$$W = nRT \ln\left(\frac{V_2$}{V_1$}\right) = 0.500 \times 8.314 \times 350 \times \ln(0.25) = - 504 J$$

Question 1

A 70.0 kg running back is moving north at 5.00 m/s and collides with an 80.0 kg linebacker moving west at 4.00 m/s. After they grab onto each other, what is the magnitude of their combined velocity immediately after the collision?

Accepted Answer

$$\sqrt{\left(\frac{70.0 	imes 5.00}{150.0}\$$right)^2$$ + \left(\frac{80.0 	imes 4.00}{150.0}\$$right)^2$$} = 2.67 m/s$$

Question 2

A 4.00 kg bomb at rest explodes into three pieces. Piece 1 (1.00 kg) flies north at 20.0 m/s, and Piece 2 (1.50 kg) flies east at 16.0 m/s. What is the magnitude of the velocity of Piece 3 immediately after the explosion?

Accepted Answer

$$\sqrt{(1.00 	imes 20.0)^2$ + (1.50 	imes 16.0)^2$} / 1.50 = 18.7 m/s$$

Question 3

Given the potential energy function $$U(x) = 2x^4$ - 8x^2$ (J, x$ in m), at which positions is the equilibrium stable?

Accepted Answer

$$x = \pm 2 m$$

Question 4

A 0.300 kg block is dropped from 0.800 m onto a spring ($$k = 500 N/m). $$What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \frac{-mg + \sqrt{(mg)^2$ + 2 k m g h}}{k} = 0.172 m$$

Question 5

An 8.00 g bullet traveling at 350 m/s embeds in a 2.00 kg block at rest on a 1.50 m-high table. What is the speed of the block+bullet immediately after the collision?

Accepted Answer

$$v = \frac{m_{bullet} v_{bullet}}{m_{block} + m_{bullet}} = 1.39 m/s$$

Question 6

An 850 kg roller coaster car starts from rest at $$h = 30.0 m on a $$frictionless track with a loop of radius $$R = 7.50 m. $$What is the speed of the car at the top of the loop?

Accepted Answer

$$v = \sqrt{2g(h - 2R)} = 16.6 m/s$$

Question 7

A 1500 kg car engine delivers $$P = 3.00 kW $$against a constant road resistance $$f = 600 N. $$What is the car's maximum (terminal) speed?

Accepted Answer

$$v_{max} = \frac{P}{f} = 5.00 m/s$$

Question 8

Two flasks are connected by a valve: Flask 1 ($$V_1 = 2.00$ L, P_1$ = 3.00$$ atm), Flask 2 ($$V_2 = 3.00$ L, P_2$ = 1.00$$ atm), both at $$T = 300 K. $$After mixing, what is the final pressure?

Accepted Answer

$$P_f = \frac{P_1$ V_1$ + P_2$ V_2$}{V_1$ + V_2$} = 1.8$$ atm

Question 9

A piston compresses 0.500 mol of ideal gas from $$V_1 = 10.0$ L to V_2$ = 2.50 L at $$constant $$T = 350 K. $$What is the work done on the gas during this compression?

Accepted Answer

$$W = nRT \ln\left(\frac{V_2$}{V_1$}ight) = 0.500 	imes 8.314 	imes 350 	imes \ln(0.25) =  - 504 J$$

Question 10

A 0.500 kg copper block ($$c = 390 J/kg K) at 200$^\circC is $$dropped into 2.00 kg of water at 20.0$$^\circC$$ ($$c_{water} = 4186 J/kg K) in an $$insulated container. What is the final equilibrium temperature?

Accepted Answer

$$T_f = \frac{m_{Cu} c_{Cu} T_{Cu} + m_w c_w T_w}{m_{Cu} c_{Cu} + m_w c_w} = 23.2^\circC$$

Question 11

How much heat is required to convert 0.200 kg of ice at $$-20.0^\circC to $$steam at $$130^\circC$$? ($$c_{ice} = 2090 J/kg K$$, $$c_{water} = 4186 J/kg K$$, $$c_{steam} = 2010 J/kg K$$; $$L_f = 3.34 	imes 10^5$ J/kg, L_v = 2.26$$ 	imes $$10^6 J/kg.)$$

Accepted Answer

$$Q = m c_{ice} \Delta T + m L_f + m c_{water} \Delta T + m L_v + m c_{steam} \Delta T = 5.94 	imes 10^5$ J

Question 12

A monatomic ideal gas ($$C_v = \frac{3R}{2}$$ per mole) undergoes a cycle: (1) isochoric heating from $$T_1 = 300$ K, p_1$ = 1.00 	imes 10^5$ Pa, V = 0.0200$ m^3$ to p_2$ = 3.00 	imes 10^5$ Pa. What is the temperature after step 1?

Accepted Answer

$$T_2$$ = $$T_1$$ \frac{$$p_2$$}{$$p_1$$} = 900$$ K

Question 13

A 0.300 kg block is dropped from 0.800 m onto a spring ($$k = 500 N/m). At $$maximum compression, what is the net upward force on the block?

Accepted Answer

$$F_{net} = kx_{max} - mg = 500 	imes 0.172 - 0.300 	imes 9.8 = 86.0 N$$

Question 14

A 8.00 g bullet at 350 m/s embeds in a 2.00 kg block on a 1.50 m-high table. How far from the base of the table does the block land?

Accepted Answer

$$d = v_{x} t = 1.39 	imes \sqrt{\frac{2 	imes 1.50}{9.8}} = 0.76 m$$

Question 15

A monatomic ideal gas ($$C_v = \frac{3R}{2}$$ per mole) undergoes a cycle. In the isothermal compression step, what is the work done by the gas if it returns to its original state?

Accepted Answer

$$W = nRT \ln\left(\frac{V_f}{V_i}\right)$$, which is negative for compression

Question 16

A 0.500 kg copper block ($$c = 390 J/kg K) at 200$^\circC is $$dropped into 2.00 kg of water at 20.0$$^\circC in an $$insulated container. How much heat did the copper lose?

Accepted Answer

$$Q_{Cu} = m_{Cu} c_{Cu} (T_f - T_{Cu}) = 0.500 	imes 390 	imes (23.2 - 200) = -34,500 J$$

Question 17

A piston compresses 0.500 mol of ideal gas from $$V_1 = 10.0$ L to V_2$ = 2.50 L at $$constant $$T = 350 K. $$The gas is then heated at constant volume until the pressure triples. What is the final temperature?

Accepted Answer

$$T_f = 3 	imes 350 = 1050 K$$

Question 18

An 850 kg roller coaster car starts from rest at $$h = 30.0 m on a $$frictionless track with a loop of radius $$R = 7.50 m. $$What is the normal force on the car at the top of the loop?

Accepted Answer

$$N = m \left(\frac{v^2$}{R} - g\right) = 850 \left(\frac{(16.6)^2$}{7.5} - 9.8\right) = 13,000 N$$

Physics Exam Practice: Momentum, Energy, Thermodynamics, and Gas Laws

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