Learn Extracted exam questions AP Physics 2 2015 Free Response
2015 Free Response
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[Figure: Cross section of a drinking glass filled with a thin layer of liquid. From top to bottom: a layer labeled "Air", then a shaded layer labeled "Liquid", then a layer labeled "Glass". The bottom right corner of the glass is a circular arc centered at point $O$, which is marked at the liquid-glass boundary directly above the arc's center. A vertical dashed line rises from $O$. Point $P$ is marked on the flat bottom (outer) surface of the glass, directly below $O$. An arrow representing a light beam comes from the lower right, aimed at $O$, making angle $\theta_1$ with the vertical dashed line at $O$.]
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 corners of the glass are circular arcs, with the bottom right arc centered at point $O$. A monochromatic light source placed to the right of point $P$ shines a beam aimed at point $O$ at an angle of incidence $\theta$. 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 $\theta = \theta_1$, 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 $\theta$ is increased.
In a coherent paragraph-length answer, describe the processes involved in the formation of spots $X$ and $Y$ when $\theta = \theta_1$. 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.
When $\theta$ is increased to $\theta_2$, one of the spots becomes brighter than it was before, due to total internal reflection.
[Figure: Same cross-section diagram as above (Air / Liquid / Glass layers, arc centered at $O$, point $P$ below), but the incident beam now makes angle $\theta_2$ with the vertical dashed line at $O$.]
On the figure below, draw a ray diagram that clearly and accurately shows the formation of spots $X$ and $Y$ when $\theta = \theta_2$.
Which spot, $X$ or $Y$, becomes brighter than it was before due to total internal reflection? Explain your reasoning.
When $\theta$ is further increased to $\theta_3$, one of the spots disappears entirely.
[Figure: Same cross-section diagram as above (Air / Liquid / Glass layers, arc centered at $O$, point $P$ below), but the incident beam now makes angle $\theta_3$ with the vertical dashed line at $O$.]
On the figure below, draw a ray diagram that clearly and accurately shows the formation of the remaining spot, $X$ or $Y$, when $\theta = \theta_3$.
Indicate which spot, $X$ or $Y$, disappears. Explain your reasoning in terms of total internal reflection.
[Circuit diagram: A battery of emf $\mathcal{E}$ is connected at the bottom of the circuit. From the battery, a wire goes up the left side to a node, then splits. Bulb 1 is in the top-left branch. After bulb 1, the wire continues right to a node where the circuit splits into two parallel branches: the upper branch contains bulb 3 in series with switch $S$ (initially open); the lower branch contains bulb 2. Both branches reconnect and return down the right side to the battery. So bulb 1 is in series with the parallel combination of (bulb 3 + switch $S$) and bulb 2.]
A battery of emf $\mathcal{E}$ 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 student makes the following prediction about bulb 1: "Bulb 1 will decrease in brightness when the switch is closed."
Do you agree or disagree with the student's prediction about bulb 1? Qualitatively explain your reasoning.
Before the switch is closed, the power expended by bulb 1 is $P_1$. Derive an expression for the power $P_{new}$ expended by bulb 1 after the switch is closed, in terms of $P_1$.
How does the result of your derivation in part (a)ii relate to your explanation in part (a)i?
A student makes the following prediction about bulb 2: "Bulb 2 will decrease in brightness after the switch is closed."
Do you agree or disagree with the student's prediction about bulb 2? Explain your reasoning in words.
Justify your explanation with a calculation.
While the switch is open, bulb 3 is replaced with an uncharged capacitor. The switch is then closed.
How does the brightness of bulb 1 compare to the brightness of bulb 2 immediately after the switch is closed? Justify your answer.
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.
Students are watching a science program about the North Pole. The narrator says that cold air sinking near the North Pole causes high air pressure. Based on the narrator's statement, a student makes the following claim: "Since cold air near the North Pole is at high pressure, temperature and pressure must be inversely related."
Do you agree or disagree with the student's claim about the relationship between pressure and temperature? Justify your answer.
After hearing the student's hypothesis, you want to design an experiment to investigate the relationship between temperature and pressure for a fixed amount of gas. The following equipment is available.
[Figure: Two labeled apparatus drawings side by side. Left: a cylindrical container with a movable piston (a rod inserted into one end of the cylinder), labeled "Cylinder with Movable Piston". Right: a cylindrical container with both ends capped/fixed, labeled "Cylinder with Fixed Lid".]
___ A cylinder with a movable piston, shown above on the left ___ A cylinder with a fixed lid, shown above on the right Note: The two cylinders have gaskets through which measurement instruments can be inserted without gas escaping. ___ A pressure sensor ___ A source of mixed ice and water ___ A basin that is large enough to hold either cylinder with a lot of extra room ___ A meterstick ___ A source of hot water ___ A thermometer ___ A stopwatch
Put a check in the blank next to each of the items above that you would need for your investigation. Outline the experimental procedure you would use to gather the necessary data. Make sure the outline contains sufficient detail so that another student could follow your procedure.
The table below shows data from a different experiment in which the volume, temperature, and pressure of a sample of gas are varied.
| Trial Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Volume (cm$^3$) | 10.0 | 5.0 | 4.0 | 3.0 | 5.0 | 4.0 | 10.0 | 5.0 | 3.0 | 4.0 | 5.0 | 10.0 | 3.0 | 5.0 |
| Pressure (kPa) | 100 | 200 | 250 | 330 | 220 | 270 | 110 | 230 | 380 | 290 | 240 | 120 | 420 | 250 |
| Temperature ($^\circ$C) | 0 | 0 | 0 | 0 | 20 | 20 | 20 | 40 | 40 | 40 | 60 | 60 | 70 | 70 |
What subset of the experimental trials would be most useful in creating a graph to determine the relationship between temperature and pressure for a fixed amount of gas? Explain why the trials you selected are most useful.
[Blank grid: a set of labeled coordinate axes (x-axis horizontal, y-axis vertical) with fine gridlines but no axis labels or numbers filled in, provided for the student to plot data.]
Plot the subset of data chosen in part (c) on the axes below. Be sure to label the axes appropriately. Draw a curve or line that best represents the relationship between the variables.
What can be concluded from your curve or line about the relationship between temperature and pressure?
[Figure: A diagram showing an "Electron Source" (small filled square) at the top, above two horizontal parallel plates (shown as pairs of horizontal line segments with a gap between the left and right portions, indicating a hole at the center of each plate). The top plate and bottom plate are separated by distance $d$ (marked with a vertical double-headed arrow on the left). An electron travels straight down through the hole in the top plate with velocity $v_0$ (arrow pointing down, at the top plate's central gap), continues down through the gap between the plates, and exits through the hole in the bottom plate with velocity $v_f$ (arrow pointing down, at the bottom plate's central gap). Note: Figure not drawn to scale.]
The apparatus shown in the figure above consists of two oppositely charged parallel conducting plates, each with area $A = 0.25 \text{ m}^2$, separated by a distance $d = 0.010 \text{ m}$. Each plate has a hole at its center through which electrons can pass. High velocity electrons produced by an electron source enter the top plate with speed $v_0 = 5.40 \times 10^6 \text{ m/s}$, take $1.49 \text{ ns}$ to travel between the plates, and leave the bottom plate with speed $v_f = 8.02 \times 10^6 \text{ m/s}$.
Which of the plates, top or bottom, is negatively charged? Support your answer with a reference to the direction of the electric field between the plates.
Calculate the magnitude of the electric field between the plates.
Calculate the magnitude of the charge on each plate.
The electrons leave the bottom plate and enter the region inside the dashed box shown below, which contains a uniform magnetic field of magnitude $B$ that is perpendicular to the page. The electrons then leave the magnetic field at point $X$.
[Figure: Same electron-source/parallel-plate diagram as above (Electron Source square, top plate, electron traveling down at $v_0$, bottom plate, electron traveling down at $v_f$), but now below the bottom plate is a dashed-line box labeled $B$ on its left edge, representing a region of uniform magnetic field perpendicular to the page. The bottom-right corner of the dashed box is labeled point $X$. Note: Figure not drawn to scale.]
On the figure above, sketch the path of the electrons from the bottom plate to point $X$. Explain why the path has the shape that you sketched.
Indicate whether the magnetic field is directed into the page or out of the page. Briefly explain your choice.