1. An insulated container with a divider in the middle contains two separated gases. Gas 1 is initially at a higher temperature than gas 2. The divider is then removed. Which of the following observations might be made over a period of time as the two gases mix together, and why?
(A) Gas 1 remains at a higher temperature than gas 2 because gas 1 started at a higher temperature.
(B) Gas 1 remains at a higher temperature than gas 2 because gas 1 started with a higher kinetic energy.
(C) On average, the molecules of gas 1 lose all of their kinetic energy to the molecules of gas 2 through collisions, resulting in gas 2 eventually having a higher temperature than gas 1.
(D) On average, the molecules of gas 1 lose some of their kinetic energy to the molecules of gas 2 through collisions, resulting in the two gases eventually having the same temperature.
2. A small amount of charge is placed on both an isolated conducting sphere and an isolated insulating sphere. For both spheres, the charge is added at a small area at the top of the sphere. After a few seconds, where on each of the spheres is the charge that was added?
4. The figure above shows three objects (X, Y, and Z) that have charges -4q , + q, and -q , respectively. The objects are held fixed on an axis at the positions shown. The magnitude of the electrostatic force exerted by object Y on object Z is F. What is the magnitude of the net electrostatic force exerted on object Y due to the other two objects?
5. The above graph shows current as a function of potential difference for two different filament lamps. If the two lamps are connected in parallel to a 3.0 V battery, what is the total current supplied by the battery?
(A) 0.5 A
(B) 0.8 A
(C) 1.0 A
(D) 1.6 A
6. An ideal gas is initially in state 1 at a temperature of 200 K. The gas is taken through the two reversible thermodynamic processes shown in the PV diagram above. The process from state 1 to state 2 is isothermal. The process from state 2 to state 3 is isobaric. What is the temperature of the gas when it is in state 3 ?
(A) 800 K
(B) 400 K
(C) 200 K
(D) 100 K
1. (10 points, suggested time 20 minutes)
The figure above shows two metal spheres that are far apart compared to their size and that are held in place. The spheres are connected by wires to either side of switch S. Initially, the switch is open. Sphere 1 has mass m1 , radius r1 , and a net positive charge +Q0. Sphere 2 has mass m2 and radius r2＜r1 and is initially uncharged. The switch is then closed. Afterward, sphere 1 has a charge Q1 and is at potential V1 , and the electric field strength just outside its surface is E1 . The corresponding values for sphere 2 are Q2 , V2 , and E2 . Neglect air resistance and gravitational interactions.
(a) i. Indicate whether V1 is larger than, smaller than, or equal to V2 . Briefly explain your reasoning using appropriate physics principles and/or mathematical models.
ii. Indicate whether Q1 is larger than, smaller than, or equal to Q2 . Briefly explain your reasoning using appropriate physics principles and/or mathematical models.
iii. Indicate whether E1 is larger than, smaller than, or equal to E2 . Show how you arrived at your answer using appropriate physics principles and/or mathematical models.
(b) The distance between the centers of sphere 1 and sphere 2 is D. The switch is now opened, the wires are disconnected from the spheres, and the spheres are released, all without changing the charges on the spheres. Write but do NOT solve equations that could be used to determine the velocities v1 and v2 of the spheres a long time after they are released, in terms of m1 , m2 , Q1 , Q2 , D, and physical constants, as appropriate.
(c) The spheres are now returned to their original locations. Sphere 1 once again has initial net charge +Q0 , and sphere 2 is initially uncharged. The switch is again closed and then reopened. Sphere 3, an uncharged metal sphere of radius r3 > r1 > r2 on an insulating handle, is now brought into contact with sphere 2. Sphere 3 is then moved away.
i. Indicate the sign of the final charge on each sphere.
ii. Rank the absolute value of the final charge on each of the three spheres. Explain how you arrived at this answer.
2. (12 points, suggested time 25 minutes)
Water flows at a speed v of 2.00 m/s through a hose of radius 3 cm and into a large empty rectangular pool. The pool has a level bottom and measures 10.0 m long by 8.00 m wide. The density of water is 1.00 × 103 kg/m3 and atmospheric pressure is 1.01 × 105 Pa . Express all numerical answers to the following parts to at least three significant figures.
(a) Calculate the total pressure exerted downward on the bottom of the pool after the water has been running for 3 hours.
(b) A small ball is floating in the water as the pool fills. Indicate whether the buoyant force on the floating ball increases, decreases, or stays the same as the amount of water in the pool increases. Briefly explain your reasoning.
(c) A person gets impatient because it is taking too long to fill the pool. The person attaches a nozzle to the end of the hose that reduces the radius of the opening to 1.5 cm. Assume the speed of the water in the hose (before it reaches the nozzle) remains at 2.00 m/s . The person claims that the water now comes out of the nozzle faster than it did from the hose without the nozzle and therefore the pool will fill faster.
i. Do you agree that the pool will fill faster? Explain your reasoning in terms of conservation principles.
ii. Calculate the speed of the water as it leaves the nozzle. Explain how your calculation is consistent with the conservation principles used in part (c)(i).
(d) When the water in the pool is 1.50 m deep, the hose is turned off. A person who is 1.80 m tall then floats in the pool.
i. Is the net downward force exerted on the bottom of the pool now greater than, less than, or the same as it was before the person got into the pool? Explain your reasoning in terms of the forces exerted on the person.
ii. Would your answer to part (d)(i) be different if the person was standing on the bottom of the pool? Explain your reasoning.
(e) Consider the total pressure exerted by the water on the sides of the pool near the bottom of the pool. When the person floats in the pool, is this pressure greater than, less than, or the same as it was before the person got into the pool? Explain your reasoning.