Learn Extracted exam questions AP Physics 2 2018 Free Response
2018 Free Response
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The figures above show a rectangular conducting loop at three instants in time. The loop moves at a constant speed $v$ into and through a region of constant, uniform magnetic field $B$ directed into the page. The magnetic field is zero outside the region.
[Three diagrams, each showing a grid of "×" symbols (magnetic field $B$ into the page) with a rectangular conducting loop moving to the right with velocity $v$. "Time $t_1$": the loop is entering the field region from the left, with its right edge just inside the field and its left edge outside the field (only partially inside the ×'s). "Time $t_2$": the loop is fully inside the field region, entirely surrounded by ×'s. "Time $t_3$": the loop is exiting the field region on the right side, with its left edge inside the field (×'s) and its right edge outside the field (no ×'s). Label "Conducting Loop" points to the rectangle at Time $t_1$.]
In a coherent paragraph-length response, compare the magnitude and direction of the current at times $t_1$, $t_2$, and $t_3$. Include an explanation of why there is or is not a current and the direction of the current if one is present. Use fundamental physics concepts and principles in your explanation.
The loop is removed. A proton traveling to the right in the plane of the page, as shown below, then enters the region of magnetic field with a speed $v = 3.0 \times 10^5$ m/s. The magnitude of the field is 0.030 T. The effects of gravity are negligible.
[Diagram: a grid of "×" symbols representing magnetic field $B$ into the page. A proton (labeled "Proton") enters from the left moving to the right with velocity $v$ into the field region. A separate coordinate-axis diagram alongside shows $x$ (to the right), $y$ (upward), and $z$ (out of the page).]
Calculate the magnitude of the force on the proton as it enters the field.
On the figure below, sketch a possible path of the proton as it travels through the magnetic field. Clearly label the path P1.
[Diagram: a grid of "×" symbols (field into the page) with a proton entering from the left moving to the right, labeled "Proton", with velocity $v$ arrow.]
A second proton now enters the magnetic field at the same point and from the same direction but at a greater speed than the first proton. On the figure above, draw the path of the second proton as it travels through the field. Clearly label the path P2.
Next an electric field is applied in the same region as the magnetic field, such that there is no net force on the first proton as it enters the region. Calculate the magnitude and indicate the direction of the electric field relative to the coordinate system shown in part (b).
[Circuit diagram: Point $A$ connects to resistor $R_1$ in series, which connects to a parallel combination of resistor $R_2$ (top branch, drawn as a zigzag resistor symbol) and a switch S (bottom branch), which then connects to point $B$.]
Students are given resistor 1 with resistance $R_1$ connected in series with the parallel combination of a switch S and resistor 2 with resistance $R_2$, as shown above. The circuit elements cannot be disconnected from each other, and other circuit components can only be connected at points $A$ and $B$. The students also are given an ammeter and one 9 V battery. The teacher instructs the students to take measurements that can be used to determine $R_1$ and $R_2$.
Complete the diagram below to show how the ammeter and the battery should be connected to experimentally determine the resistance of each resistor. Describe the experiment by listing the measurements to be taken and explaining how the measurements would be used to calculate resistances $R_1$ and $R_2$.
Complete the Diagram / Describe the Experiment
[Diagram: the same circuit ($A$—$R_1$—[$R_2$ parallel with switch S]—$B$) is shown blank, for the student to add the ammeter and battery connections.]
A second group of students is given a combination of circuit elements that is similar to the previous one but has an initially uncharged capacitor in series with the open switch, as shown above. [Diagram: circuit $A$—$R_1$—[$R_2$ parallel with (switch S in series with a capacitor)]—$B$.] The combination is placed in a circuit with a power supply so that the potential difference between $A$ and $B$ is maintained at 9 V. The students close the switch and immediately begin to record the current through point $B$. The initial current is 0.9 A, and after a long time the current is 0.3 A.
Compare the currents through resistor 1, resistor 2, and the switch immediately after the switch is closed to the currents a long time after the switch is closed. Specifically state if any current is zero.
Calculate the values of $R_1$ and $R_2$.
Determine the potential difference across the capacitor a long time after the switch is closed.
A third group of students now uses the combination of circuit elements with the capacitor. They connect it to a 9 V battery that they treat as ideal but which is actually not ideal and has internal resistance.
How does the third group's value of $R_1$ calculated from the data they collected compare to the second group's value? Explain your reasoning with reference to physics principles and/or mathematical models.
[Diagram: arrows labeled "Light" shine diagonally down onto a rectangular block labeled "Metal"; small circles labeled "Electrons" are shown being emitted upward and diagonally from the metal surface.]
Monochromatic light of frequency $f$ shines on a metal, as shown above. The frequency of the light is varied, and for some frequencies electrons are emitted from the metal. The maximum kinetic energy $K_e$ of the emitted electrons is measured as a function of the frequency of the light.
Based on conservation of energy, the relationship between $K_e$ and $f$ is predicted to be $Af = B + K_e$ when $f > f_0$ and $K_e = 0$ when $f \le f_0$, where $A$ and $B$ are positive constants. A graph of this relationship is shown below. Indicate which aspects of the graph correspond to $A$ and $B$. Also, explain the physical meaning of $A$, $B$, and $f_0$.
[Graph of $K_e$ (y-axis) vs. $f$ (x-axis); the curve is flat at $K_e = 0$ from the origin $O$ up to $f_0$ on the x-axis, then rises linearly with positive slope for $f > f_0$.]
Explain the physical meaning of the horizontal section of the graph between the origin and $f_0$.
A second metal with different properties than the first metal is now used. On the figure below, the dashed lines are the same lines shown in the previous graph. Sketch lines on the figure below that could represent the data for the second metal. Explain one difference between the two graphs.
[Graph of $K_e$ (y-axis) vs. $f$ (x-axis), with dashed lines showing the flat-then-linear relationship from part (a)(i), flat at $K_e=0$ from $O$ to $f_0$ then rising linearly beyond $f_0$; blank space for the student to sketch a second set of lines for the second metal.]
The figure below shows an electroscope. A sphere is connected by a vertical bar to the leaves, which are thin, light strips of material. The sphere, leaves, and bar are all made of metal. The electroscope initially has a negative charge, so the leaves are separated.
[Diagram: arrows labeled "Light" shine diagonally onto a circle labeled "Sphere" at the top of a vertical bar; the bar leads down into a rectangular box containing two thin vertical strips labeled "Leaves", shown separated/spread apart.]
Ultraviolet (UV) light shines on the sphere, causing the leaves of the electroscope to move closer together. Explain why this happens.
Green light then shines on an identical negatively charged electroscope. No movement of the leaves is observed. Explain why the green light does not make the leaves move, while the UV light does.
The brightness of the green light is increased until the intensity (power per unit area) is the same as that of the UV light. What aspect of the green light changes when its brightness is increased? Would shining the brighter green light on the electroscope result in movement of the leaves? Explain why or why not.
[Diagram: a large boat viewed from above/side, labeled with an arrow pointing to steel bars stacked on its deck, labeled "Steel Bars". A small cabin structure sits at the rear of the boat.]
A large boat like the one shown above has a mass $M_b$ and can displace a maximum volume $V_b$. The boat is floating in a river with water of density $\rho_{water}$ and is being loaded with steel beams each of density $\rho_{steel}$ and volume $V_{steel}$. The boat owners want to be able to carry as many beams as possible.
Derive an expression for the maximum number $N$ of steel beams that can be loaded on the boat without exceeding the maximum displaced volume, in terms of the given quantities and physical constants, as appropriate.
The captain realizes that oil is leaking from the boat, creating a thin film of oil on the water surface. In one area of the oil film the surface looks mostly green. Explain in detail how constructive interference contributes to the green appearance. Assume the index of refraction of the oil is greater than the index of refraction of the water.
Later the boat is floating down the river with the water current, heading for a town. The river has a width of 60 m and a constant depth and flows at a speed of $5$ km/hr. Partway to the town, the river narrows to a width of 30 m while its depth remains the same. Calculate the speed of the water in the narrow section.