4. A 100-g cube of ice at 0°C is dropped into 1.0 kg of water that was originally at 80°C. What is the final temperature of the water after the ice melts? You may find the following information useful: c_water = 4186 J/kg·°C, L_{f water} = 3.33 × 10⁵ J/kg.
(A) 0 °C
(B) 18 °C
(C) 32 °C
(D) 44 °C
(E) 65 °C

5. A 50.0-g object is attached to a horizontal spring with a spring constant of 10.0 N/m and released from rest with an amplitude of 25.0 cm. What is the speed of the object when it is halfway to the equilibrium position if the surface is frictionless? (A) 4.21 m/s (B) 8.42 m/s (C) 3.06 m/s (D) 6.12 m/s (E) 9.68 m/s

6. A person swings on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency. If, instead, two people sit on the swing, the new natural frequency of the swing is (A) four times greater (B) twice greater (C) the same (D) twice smaller (E) impossible to determine

7. A 70-kg log falls from a height of 25 m into a lake. Suppose the log, the lake, and the air are all at 300 K. What is the change in the entropy of the Universe for this process, assuming that all of the log's potential energy is converted into heat? (A) 57 J/K (B) 29 J/K (C) 13 J/K (D) 7 J/K (E) 0 J/K

8. A heat engine operates in a Carnot cycle between 80.0°C and 350°C. It absorbs 21,000 J of energy per cycle from the hot reservoir. The duration of each cycle is 1.0 s. What is the mechanical power output of this engine? (A) 21.0 kW (B) 91.0 kW (C) 9.10 kW (D) 16.2 kW (E) not enough information

9. A 1.5-kg copper block is given an initial speed of 3.0 m/s on a rough horizontal surface. Because of friction, the block finally comes to rest. If the block absorbs 85% of its initial kinetic energy as internal energy, calculate its increase in temperature. You may find this information useful: ccopper = 387 J/kg·°C. (A) 1.1 °C (B) 11 °C (C) 5.5 °C (D) 3.3×10⁻³ °C (E) 9.9×10⁻³ °C

10. A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is -20.0°C. How much longer is the wire on a summer day when Tc = 35.0°C? Assume that the thermal coefficient of copper is constant throughout this range at its room temperature value. The average coefficient of linear expansion for copper is 17 × 10⁻⁶ (°C)⁻¹. (A) 3.27 cm (B) 4.12 cm (C) 1.00 cm (D) 12.04 cm (E) 8.40 cm

11. A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.20 m/s in 0.832 s. What are the magnitudes of the linear impulse and the average total force experienced by a 70.0-kg passenger in the car during this time? (A) 245 kg m/s² and 438 N (B) 364 kg m/s² and 438 N (C) -245 kg m/s² and 4.38 N (D) 2.45 kg m/s² and 4.38 N (E) 245 kg m/s² and 4.38 N

12. A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm³. (The pod is dry inside.) If the pod has a radius of 6.00 cm and negligible mass, what is the mass of the frog? (A) 0.611 g (B) 0.611 kg (C) 0.350 kg (D) 1.010 kg (E) 1.010g

13. An inductor has a 54 Ohm reactance at 60 Hz. What will be the peak current if this inductor is connected to a 50 Hz source that produces 100 V rms voltage? (A) 0.69 A (B) 1.41 A (C) 2.71 A (D) 3.14 A (E) 1.73 A

14. An inductor and a resistor are connected in series. When connected to a 60 Hz, 80 V source, the voltage drop across the resistor is found to be 35 V rms and the power dissipated in the circuit is 11 W. What is the value of the resistance? (A) 134 Ω (B) 151 Ω (C) 123 Ω (D) 97 Ω (E) 111 Ω

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