Learn Extracted exam questions AP Physics 2 2021 Free Response
2021 Free Response
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A sample of ideal gas is taken through the thermodynamic cycle shown above. Process C is isothermal.
[Graph: Pressure ($\times 10^3$ Pa) on the y-axis (gridlines at 25, 50, 75, 100, 125) vs. Volume ($\times 10^{-3}$ m$^3$) on the x-axis (gridlines at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5). State 1 is at approximately $(1.0, 100)$. Process A is a horizontal arrow from state 1 at $(1.0, 100)$ to state 2 at $(4.0, 100)$, pointing right. Process B is a vertical arrow from state 2 at $(4.0, 100)$ down to state 3 at $(4.0, 25)$, pointing down. Process C is a curve from state 3 at $(4.0, 25)$ back to state 1 at $(1.0, 100)$, passing through a labeled point near $(2.1, 42)$, with an arrow pointing up and to the left toward state 1.]
Consider the portion of the cycle that takes the gas from state 1 to state 3 by processes A and B. Calculate the magnitude of the following and indicate the sign of any nonzero quantities.
- The net change in internal energy $\Delta U$ of the gas
- The net work $W$ done on the gas
- The net energy $Q$ transferred to the gas by heating
Consider isothermal process C.
Compare the magnitude and sign of the work $W$ done on the gas in process C to the magnitude and sign of the work in the portion of the cycle in part (a). Support your answer using features of the graph.
Explain how the microscopic behavior of the gas particles and changes in the size of the container affect interactions on the microscopic level and produce the observed pressure difference between the beginning and end of process C.
Consider two samples of the gas, each with the same number of gas particles. Sample 2 is in state 2 shown in the graph, and sample 3 is in state 3 shown in the graph. The samples are put into thermal contact, as shown above.
[Diagram: two adjacent boxes labeled "Sample 2 State 2" and "Sample 3 State 3", placed in contact with each other.]
Indicate the direction, if any, of energy transfer between the samples. Support your answer using macroscopic thermodynamic principles.
[Diagram: a cylindrical container with a movable piston. A downward-pointing arrow labeled "Cylinder" points to the outer container wall, and a downward-pointing arrow labeled "Piston" points to a shaded disk (the piston) inside the cylinder near the top.]
A group of students design an experiment to investigate the relationship between the density and pressure of a sample of gas at a constant temperature. The gas may or may not be ideal. They will create a graph of density as a function of pressure. They have the following materials and equipment.
- A sample of the gas of known mass $M_g$ in a sealed, clear, cylindrical container, as shown above, with a movable piston of known mass $m_p$
- A collection of objects each of known mass $m_o$
- A meterstick
Describe the measurements the students should take and a procedure they could use to collect the data needed to create the graph. Specifically indicate how the students could keep the temperature constant. Include enough detail that another student could follow the procedure and obtain similar data.
Determine an expression for the absolute pressure of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
Determine an expression for the density of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
[Graph: Density on the y-axis vs. Pressure on the x-axis, no numerical scale shown. Data points form a curve starting near the lower left, rising steeply at first, then curving to rise more gradually (concave down) as pressure increases, ending near the upper right.]
The graph above represents the students' data. Does the data indicate that the gas is ideal? Describe the application of physics principles in an analysis of the graph that can be used to arrive at your answer.
Another group of students propose that the relationship between density and pressure could also be obtained by filling a balloon with the gas and submerging it to increasing depths in a deep pool of water.
Why could submerging the balloon to increasing depths be useful for determining the relationship between the density and pressure of the gas?
[Diagram: a hand pushing down on a shaded spherical balloon submerged in water. The balloon is labeled with $V_b, \rho_g$ inside it, $\rho_w$ labeled outside to the right (the surrounding water), and $m_b$ (Balloon only, not gas) labeled below with an arrow pointing to the balloon.]
The balloon is kept underwater in the deep pool by a student pushing down on the balloon, as shown above. Let $V_b$ represent the volume of the inflated balloon, $m_b$ represent the mass of just the balloon (not including the mass of the gas), $\rho_g$ represent the density of the gas in the balloon, and $\rho_w$ represent the density of the water. Derive an expression for the force the student must exert to hold the balloon at rest under the water, in terms of the quantities given in this part and physical constants, as appropriate.
[Graph 1: axes with $B$ (vertical) vs. $I$ (horizontal). Dashed horizontal lines at $B_1$ (labeled "$B_1$ (Out of Page)") and at $-B_1$ (labeled "$-B_1$ (Into Page)"), with corresponding dashed vertical lines at $I_1$ and $-I_1$. A straight line of positive slope passes through the origin $O$ and through the points $(-I_1, -B_1)$ and $(I_1, B_1)$.]
An electromagnet produces a magnetic field that is uniform in a certain region and zero outside that region. The graph above represents the field as a function of the current in the electromagnet, with positive field directed out of the page and negative field directed into the page.
[Diagram: an upward-pointing arrow labeled "Velocity" and a leftward-pointing arrow labeled "$F_B$", both attached to a point labeled "Particle".]
The current in the electromagnet is set at $0.5I_1$. When a charged particle in the region moves toward the top of the page, the force exerted on it by the field is $F_B$ toward the left, as shown above. What changes to the current in the electromagnet could make the magnitude of the force exerted on the particle equal to $2F_B$ and the direction of the force to the right? Support your answer using physics principles.
[Diagram: a circular loop of wire containing a grid of dots (representing a magnetic field out of the page), with a circle labeled "Bulb" on the left side of the loop, and an arrow labeled "$B$" pointing to the top-right of the loop's boundary.
Graph 2: axes with $B_1$ (vertical, dashed line above origin) vs. $t$ (horizontal), with dashed vertical lines at $t_1, t_2, t_3, t_4$ and a dashed horizontal line at $-B_1$ below the origin. The plotted curve starts at $B_1$ for $t < t_1$, decreases linearly crossing zero and continuing down to $-B_1$ by $t_2$, remains constant at $-B_1$ from $t_2$ to $t_3$, then increases linearly back up to $B_1$ by $t_4$ and remains constant at $B_1$ after $t_4$.
Graph 3: axes with Energy (vertical) vs. $t$ (horizontal), with dashed vertical lines at $t_1, t_2, t_3, t_4$. The plotted curve is flat (zero slope, cumulative energy constant) for $t < t_1$, then rises with increasing (concave-up) slope from $t_1$ to $t_2$, continues rising linearly (constant slope) from $t_2$ to $t_3$, then flattens out (zero slope, constant) after $t_3$ through $t_4$ and beyond.]
A circuit is made by connecting an ohmic lightbulb of resistance $R$ and a circular loop of area $A$ made of a wire with negligible resistance. The circuit is placed with the plane of the loop perpendicular to the field of the electromagnet, as shown above on the left. The magnetic field changes as a function of time, as shown in Graph 2. The bulb dissipates energy during the interval $t_1 < t < t_3$. Graph 3 below shows the cumulative energy dissipated by the bulb (the total energy dissipated since $t = 0$) as a function of time.
The original bulb is replaced by a new ohmic lightbulb with a greater resistance, but everything else stays the same. How would the cumulative energy graph for the new bulb be different, if at all, from Graph 3 above? Support your answer using physics principles.
The new lightbulb is removed and replaced by the original lightbulb. The magnetic field now changes from $2B_1$ to $-2B_1$ during the same interval $t_1 < t < t_3$. A new cumulative energy graph is created for this situation. How would the new graph be different, if at all, from Graph 3? Support your answer using physics principles.
A student derives the following expression for the cumulative energy dissipated by the original bulb during the interval $t_1 < t < t_3$ and with the original change in magnetic field shown in Graph 2.
Whether or not the equation is correct, does the functional dependence of cumulative energy on the elapsed time $(t_3 - t_1)$ make physical sense? Support your answer using physics principles.
Light and matter can be modeled as waves or as particles. Some phenomena can be explained using the wave model, and others can be explained using the particle model.
Calculate the speed, in m/s, of an electron that has a wavelength of 5.0 nm.
The electron is moving with the speed calculated in part (a) when it collides with a positron that is at rest. A positron is a particle identical to an electron except that its charge is positive. The two particles annihilate each other, producing photons. Calculate the total energy of the photons.
[Diagram: on the left, a wavy arrow labeled "Photon" moving right toward a dot labeled "Electron", captioned "Before Collision". On the right, a dot labeled "Electron" with a straight arrow pointing up and to the right, captioned "After Collision (Photon not shown)".]
A photon approaches an electron at rest, as shown above on the left, and collides elastically with the electron. After the collision, the electron moves toward the top of the page and to the right, as shown above on the right, at a known speed and angle. In a coherent, paragraph-length response, indicate a possible direction for the photon that exists after the collision and its frequency compared to that of the original photon. Describe the application of physics principles that can be used to determine the direction of motion and frequency of the photon that exists after the collision.