Learn Extracted exam questions AP Physics 2 2017 Free Response
2017 Free Response
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Two students observe water flowing from left to right through the section of pipe shown above, which decreases in diameter and increases in elevation. The pipe ends on the right, where the water exits vertically. At point $A$ the water is known to have a speed of $0.50\ \text{m/s}$ and a pressure of $2.0 \times 10^{5}\ \text{Pa}$. The density of water is $1000\ \text{kg/m}^3$.
[Diagram: A section of horizontal pipe with a valve (wheel handle) near the left end. The pipe has diameter $2.5$ cm at the left section (where point $A$ is located, $10$ m to the right of the valve), then bends and rises, decreasing to diameter $1.5$ cm at point $B$ near the top right, where the water exits vertically upward out of the open pipe end. Point $B$ is located $1$ m below the top opening of the vertical pipe, and the vertical pipe extends $5$ m above the level of point $A$. Note: Figure not drawn to scale.]
The students disagree about the water pressure and speed at point $B$. They make the following claims.
Student $Y$ claims that the pressure at point $B$ is greater than that at point $A$ because the water is moving faster at point $B$.
Student $Z$ claims the speed of the water is less at point $B$ than that at point $A$ because by conservation of energy, some of the water's kinetic energy has been converted to potential energy of the Earth-water system.
i. Indicate any aspects of student $Y$'s claim that are correct.
ii. Indicate any aspects of student $Y$'s claim that are incorrect. Support your answer using appropriate physics principles.
iii. Indicate any aspects of student $Z$'s claim that are correct.
iv. Indicate any aspects of student $Z$'s claim that are incorrect. Support your answer using appropriate physics principles.
Calculate the following at point $B$.
The speed of the water
Calculate the following at point $B$.
The pressure in the pipe
A valve to the left of point $A$ now closes off that end of the pipe. The section of pipe shown is still full of water, but the water is no longer flowing.
Calculate the absolute pressure at point $A$ (the pressure that includes the effect of the atmosphere).
An air bubble forms at point $A$. On the figure below, where the dot represents the air bubble, draw a free-body diagram showing and labeling the forces (not components) exerted on the bubble. Draw the relative lengths of all vectors to reflect the relative magnitudes of the forces.
[Figure: A dashed grid with a single filled black dot at the center, representing the air bubble at point $A$, on which the free-body diagram is to be drawn.]
A group of students is given several long, thick, cylindrical conducting rods of the same unknown material with various lengths and diameters and asked to experimentally determine the resistivity of the material using a graph. The available equipment includes a voltmeter, an ammeter, connecting wires, a variable-output DC power supply, and a metric ruler.
Describe a procedure the students could use to collect the data needed to create the graph, including the measurements to be taken and a labeled diagram of the circuit to be used. Include enough detail that another student could follow the procedure and obtain similar data.
Draw a labeled diagram here.
Write your procedure here.
Describe how the data could be graphed in a way that is useful for determining the resistivity of the material. Describe how the graph could be analyzed to calculate the resistivity.
The students are now given a rectangular rod of the material, as shown below, whose dimensions are not known. The students are asked to experimentally determine the resistance of the rod. They obtain the data in the table below for the potential difference $\Delta V$ across the rod and the current $I$ in it.
[Figure: A rectangular conducting rod shown in 3D perspective view.]
| $\Delta V$ (V) | 6.0 | 5.0 | 3.5 | 2.5 | 2.0 | 1.5 |
|---|---|---|---|---|---|---|
| $I$ (A) | 0.078 | 0.070 | 0.044 | 0.036 | 0.027 | 0.018 |
On the axes below, plot the data so that the resistance of the rectangular rod can be determined from a best-fit line. Label and scale the axes. Use the best-fit line to determine the resistance of the rod, clearly showing your calculations.
[Graph: A blank grid with labeled axes (axis titles and scale to be added by the student), horizontal axis extending right and vertical axis extending up from the origin, for plotting $\Delta V$ vs. $I$ (or $I$ vs. $\Delta V$) data.]
After completing their calculations, the students begin to consider the factors that might have produced uncertainties in their results.
The students realize that they did not take into account the internal resistance of the power supply. Briefly describe how this would affect their value of the resistance of the rectangular rod. Explain your reasoning.
The students realize that they did not take into account a possible change in the temperature of the cylindrical rods. Should the students be concerned about this? Explain why or why not.
[Diagram: An optical bench setup shown in 3D perspective. From left to right along a ruled track: a vertical screen with a ruled scale at the left end, a convex lens (drawn as an ellipse/ring) mounted upright in the middle, and a light box with a plate on its hidden side at the right end. A callout points from the light box to a small square labeled "Plate on Hidden Side of Box" showing an arrow and a bar-with-circle cutout shape. Labels: "Screen", "Convex Lens", "Light Box with Plate".]
Some students are asked to determine the focal length of a convex lens. They have the equipment shown above, which includes a waterproof light box with a plate on one side, a lens, and a screen. The box has a bright light inside, and the plate on the side has shapes cut out of it through which the light shines to create a bright object. This particular plate has a cutout that is a vertical arrow and a horizontal bar with a circle at one end. In the view shown above, the circle is near the right edge of the plate.
With the screen and light box on opposite sides of the lens, the box is aligned so that the plate is 20 cm from the center of the lens, and an image of the arrow and bar is formed on the screen. The students find that the image is clear on the screen when the screen is 30 cm from the center of the lens.
On the figure below, sketch how the image on the screen appears to the students.
[Figure: A blank rectangular screen outline with a ruled scale down its right edge (tick marks), for the student to sketch the observed image.]
Calculate the focal length of the lens.
Calculate the magnitude of the magnification of the image.
In the side view below, the arrow represents the bright object created by the plate. Draw a ray diagram on the figure below that is consistent with your calculations in parts (b)(i) and (ii). Show at least two rays, as well as the location and orientation of the image.
[Figure: A horizontal optical axis numbered from $-40$ to $40$ in increments of 10, with a thin convex lens drawn vertically at the origin (position 0) and an upward-pointing arrow (the object) at position $20$ on the axis, representing the object placed 20 cm from the lens.]
Explain how your diagram is consistent with your calculated focal length and magnification in parts (b)(i) and (ii).
The entire apparatus is now submerged in water, whose index of refraction is greater than that of air but less than that of the lens.
The figures below show cross sections of the top portion of the convex lens in air and the convex lens in water. An incident ray is shown in both cases. On each figure, draw the ray as it passes through the lens and back into the air or water.
[Figure: Two side-by-side diagrams, each showing the cross section of the top (curved) portion of a convex (plano-convex-like, rounded-top) lens shape. The left diagram is labeled "Cross Section of Lens in Air" with a horizontal incident ray arrow approaching the curved surface from the left. The right diagram is labeled "Cross Section of Lens in Water" with an identical horizontal incident ray arrow approaching the curved surface from the left. Both lens outlines are otherwise identical and unshaded.]
Describe how the focal length of the lens and the position and size of the image formed by the lens when it is in the water compare to when the lens is in air. Explain how the rays drawn in the figures in part (d)(i) support your answer.
[Figure: A square with a charged object at each corner: top-left corner $+2Q$, top-right corner $+Q$, bottom-left corner $-2Q$, bottom-right corner $+2Q$. Point $P$ is at the center of the square, with a dotted line segment of length $d$ drawn from the top-left corner ($+2Q$) to point $P$.]
The figure above represents four objects, with charges as shown, that are held in place at the corners of a square. Point $P$ is at the center of the square, a distance $d$ from each of the objects. Express all algebraic answers to the following in terms of $Q$, $d$, and physical constants.
On the dot below, draw an arrow that represents the direction of the net electric force exerted on the object with charge $+Q$ by the other three objects.
[Figure: A dot labeled $+Q$ at the intersection of a horizontal dashed line and a vertical dashed line, for the student to draw a force-direction arrow from the dot.]
Calculate the magnitude of the electric field at point $P$ due to all four objects. On the dot below, draw an arrow to indicate the direction of the net field at point $P$.
[Figure, left "Draw Arrow": A dot labeled $P$ at the intersection of a horizontal dashed line and a vertical dashed line, for the student to draw a field-direction arrow from the dot. Right "Calculate Electric Field": blank space for the calculation.]
Calculate the electric potential at point $P$ due to all four objects.
In a coherent, paragraph-length response, briefly describe the meaning of electric potential energy and explain qualitatively how electric potential energy can be related to work. Also explain qualitatively how the electric potential energy of the four-object system would change if the $+Q$ and $+2Q$ objects on the right side of the square now switch positions as shown in the figure below. Support your explanation using appropriate physics principles.
[Figure: A square with a charged object at each corner, showing the swapped configuration: top-left corner $+2Q$, top-right corner $+2Q$, bottom-left corner $-2Q$, bottom-right corner $+Q$. Point $P$ is at the center of the square, with a dotted line segment of length $d$ drawn from the top-left corner ($+2Q$) to point $P$.]