1. Three objects — X, Y, and Z-are each given an excess electric charge. The objects are then brought near each other in pairs but do not touch. It is found that X and Y attract each other, Y and Z repel, and X and Z attract. Which of the following is a correct conclusion about the signs of the charges that can be drawn from these observations?
(A) X and Y have charges of the same sign, and Z has a charge of the opposite sign.
(B) X and Z have charges of the same sign, and Y has a charge of the opposite sign.
(C) Y and Z have charges of the same sign, and X has a charge of the opposite sign.
(D) X, Y, and Zall have charges of the same sign.
2. Each of the figures below shows the path of a charged particle moving in the plane of the page in a magnetic field that is perpendicular to the page. If the mass, speed, and charge of the particles are the same, in which case does the field have the greatest magnitude?
3. The figure above shows pipe 1 of cross-sectional area A1 and pipe 2 of cross-sectional area A2 , which merge into pipe 3 of cross-sectional area A3. The water in pipes 1 and 2 flows with speeds v1 and v2 , respectively. What is the speed of the water in pipe 3 ?
4. A hollow rectangular box is filled with a liquid and can be placed in any of the three orientations shown above. In which orientation will the fluid pressure at the bottom of the box be greatest, and why?
(A) Orientation X, because pressure at the bottom of a fluid is greater when the vertical height of the fluid is greater
(B) Orientation Y, because pressure at the bottom of a fluid is greater when the width times the height of the fluid is greater
(C) Orientation Z, because pressure at the bottom of a fluid is greater when the area of the bottom surface is greater
(D) All three orientations have the same pressure, because the weight of the fluid is the same in each case.
1. (10 points - suggested time 20 minutes)
The figure above shows a cross section of a drinking glass (index of refraction 1.52) filled with a thin layer of liquid (index of refraction 1.33). The bottom comers of the glass are circular arcs, with the bottom right arc centered at point ο. A monochromatic light source placed to the right of point P shines a beam aimed at point ο at an angle of incidence θ . The flat bottom surface of the glass containing point P is frosted so that bright spots appear where light from the beam strikes the bottom surface and does not reflect. When θ=θ1,two bright spots appear on the bottom surface of the glass. The spot closer to point P will be referred to as X; the spot farther from P will be referred to as Y. The location of spot X and that of spot Y both change as θ is increased.
(a) In a coherent paragraph-length answer, describe the processes involved in the formation of spots X and Y when θ = θ1 . Include an explanation of why spot Y is located farther from point P than spot X is and what factors affect the brightness of the spots.
(b) When θ is increased to θ2, one of the spots becomes brighter than it was before, due to total internal reflection.
i On the figure below, draw a ray diagram that clearly and accurately shows the formation of spots X and Y when θ = θ2.
ii. Which spot, X or Y, becomes brighter than it was before due to total internal reflection? Explain your reasoning.
(c) When θ is further increased to θ3, one of the spots disappears entirely.
i. On the figure below, draw a ray diagram that clearly and accurately shows the formation of the remaining spot, X or Y when θ = θ3 .
ii. Indicate which spot, X or Y, disappears. Explain your reasoning in terms of total internal reflection.
2. (12 points, suggested time 25 minutes)
A battery of emf ε and negligible internal resistance, three identical incandescent lightbulbs, and a switch S that is initially open are connected in the circuit shown above. The bulbs each have resistance R. Students make predictions about what happens to the brightness of the bulbs after the switch is closed.
(a) A student makes the following prediction about bulb 1: "Bulb 1 will decrease in brightness when the switch is closed"
i. Do you agree or disagree with the student's prediction about bulb 1 ? Qualitatively explain your reasoning.
ii. Before the switch is closed, the power expended by bulb 1 is P1. Derive an expression for the power Pnew expended by bulb 1 after the switch is closed in terms of P1
iii. How does the result of your derivation in part (a)ii relate to your explanation in part (a)i?
(b) A student makes the following prediction about bulb 2: "Bulb 2 will decrease in brightness after the switch is closed"
i. Do you agree or disagree with the student's prediction about bulb 2 ? Explain your reasoning in words.
ii. Justify your explanation with a calculation.
(c) While the switch is open, bulb 3 is replaced with an uncharged capacitor. The switch is then closed.
i. How does the brightness of bulb 1 compare to the brightness of bulb 2 immediately after the switch is closed? Justify your answer.
ii. How does the brightness of bulb 1 compare to the brightness of bulb 2 a long time after the switch is closed? Justify your answer.