AP PHYSICS 1
Test Booklet
Experiment Design FRQ
1.
The apparatus shown above consists of two identical springs of negligible mass, each with spring constant k =
20.4 N/m and each attached at one end to a vertical rotating pole. Identical small spheres of mass m are attached to
the other ends of the springs. The spheres are constrained to horizontal motion by horizontal guides of negligible
friction, each of which has a ruler below it for measuring the radial position r of the sphere. The system can be
manually rotated about the pole’s axis. In a lab experiment, a student adjusts the rotational speed so that the
spheres move to a desired radius r. For each such value of r, the student measures the rotational period T. The
student’s partially completed data table is shown below. The length of each unstretched spring is L = 0.15 m.
(a) Calculate the missing values from the table above. Show your work in the space below
(b) On the axes below, plot the data points for the spring force Fspring as a function of the acceleration ac. Label
the axes, including the scale. Draw a straight line that best represents the data
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Test Booklet
Experiment Design FRQ
(c)
i. Calculate the slope of your line.
ii. Indicate what the slope calculated in part (c)-i represents.
(d) One sphere and one spring are removed from the rotation apparatus. They are hung vertically so that the sphere
is now suspended from the spring, as shown below.
i. Describe a procedure you could use, and the measurements you would make, to verify the value obtained
in part (c) using the setup shown above.
ii. Show how you would use the measurements described in part (d)-i to verify the value obtained in part
(c).
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AP Physics 1
Test Booklet
Experiment Design FRQ
2.
This question is a long free-response question. Show your work for each part of the question.
(
points, suggested time
minutes)
A company selling a type of spring makes the following claim: “The elastic potential energy that the spring is
capable of storing for a given compression distance does not decrease, even after the spring compresses and/or
stretches hundreds of times.” The students in a physics class have decided to test the company’s claim.
(a)
i. State a basic physics principle or law the students could use in designing an experiment to test the company’s
claim.
ii. Using the principle or law stated in part (a)i, determine an equation for the elastic potential energy stored in the
spring in terms of quantities that can be obtained from measurements made with equipment usually found in a
school physics laboratory.
(b) Design an experimental procedure the students could use to collect the data needed to test the company’s
claim. Assume equipment usually found in a school physics laboratory is available.
In the table below, list the quantities and associated symbols that would be measured in your experiment and the
equipment used to measure them. Also list the equipment that would be used to measure each quantity. You do not
need to fill in every row. If you need additional rows, you may add them to the space just below the table.
Quantity to Be Measured
Symbol for Quantity
Equipment for Measurement
Describe the overall procedure to be used, referring to the table. Provide enough detail so another student could
replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the
symbols defined in the table and/or include a simple diagram of the setup.
(c) Explain how the students should analyze the data to determine whether the company’s claim is true, i.e.,
whether the energy stored by the spring for a given compression distance does not decrease after the spring has
compressed and/or stretched hundreds of times.
(d) The students also investigate two springs, spring and spring , made by another company. The students
hang spring vertically, attaching blocks of various known masses from the bottom end of the spring and
measuring the total length of the spring for each block. The students graph the spring length as a function of
hanging mass and draw the line of best fit, as shown below.
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Test Booklet
Experiment Design FRQ
i. The students follow the same procedure using spring , which has the same equilibrium length as spring but
stores more energy than spring for a given displacement. On the graph above, sketch what the line of best fit
could look like for the data obtained using spring .
ii. The students attach a block to spring and let it hang at rest. The students pull the block down by
,
release it, and measure the time interval
for one oscillation. The students then repeat the procedure, but pull
the block down by
instead of
. For which initial displacement, if either, is
greater?
is greater for the
displacement.
is greater for the
displacement.
is the same in both cases.
Briefly explain your reasoning.
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AP Physics 1
Test Booklet
Experiment Design FRQ
3.
A new kind of toy ball is advertised to “bounce perfectly elastically” off hard surfaces. A student suspects,
however, that no collision can be perfectly elastic. The student hypothesizes that the collisions are very close to
being perfectly elastic for low-speed collisions but that they deviate more and more from being perfectly elastic as
the collision speed increases.
a. Design an experiment to test the student’s hypothesis about collisions of the ball with a hard surface. The
student has equipment that would usually be found in a school physics laboratory.
i. What quantities would be measured?
ii. What equipment would be used for the measurements, and how would that equipment be used?
iii. Describe the procedure to be used to test the student’s hypothesis. Give enough detail so that
another student could replicate the experiment.
b. Describe how you would represent the data in a graph or table. Explain how that representation would be
used to determine whether the data are consistent with the student’s hypothesis.
c. A student carries out the experiment and analysis described in parts (a) and (b). The student immediately
concludes that something went wrong in the experiment because the graph or table shows behavior that is
elastic for low-speed collisions but appears to violate a basic physics principle for high-speed collisions.
i. Give an example of a graph or table that indicates nearly elastic behavior for low-speed
collisions but appears to violate a basic physics principle for high-speed collisions.
ii. State one physics principle that appears to be violated in the graph or table given in part (c)i.
Several physics principles might appear to be violated, but you only need to identify one.
Briefly explain what aspect of the graph or table indicates that the physics principle is violated,
and why.
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Test Booklet
Experiment Design FRQ
4.
This question is a long free-response question. Show your work for each part of the question.
Two carts, cart and cart , are initially at rest and placed next to each other on a horizontal track, as shown in
Figure 1. A switch on top of cart can be pressed so that a compressed spring inside of the cart expands and
pushes a plunger outward, causing the two carts to recoil, as shown in Figure 2. Both carts have identical but
unknown masses, . The carts are designed so that bars of additional but unknown mass can be added and
secured to the carts. A group of students are asked to determine the relationship of the momentum of the cart
–bar system to the momentum of the cart –bar system immediately after recoil. The students have access to
equipment that can be found in a typical school physics laboratory.
(a)
i. State a basic physics principle or law that the students could use to determine the relationship of the momentum
of the cart –bar system to the momentum of the cart –bar system immediately after recoil.
ii. Using the principle or law stated in part (a)(i), determine an equation for the relationship of the momentum of
the cart –bar system to the momentum of the cart –bar system immediately after recoil in terms of quantities
that can be obtained from measurements.
(b) Design an experimental procedure that the students could use to determine the relationship of the momentum
of the cart –bar system to the momentum of the cart –bar system immediately after recoil.
In the table below, list the quantities and associated symbols that would be measured in your experiment and the
equipment used to measure them. Also list the equipment that would be used to measure each quantity. You do not
need to fill in every row. If you need additional rows, you may add them to the space just below the table.
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AP Physics 1
Test Booklet
Experiment Design FRQ
Quantity to be Measured
Symbol for Quantity
Equipment for Measurement
Describe the overall procedure to be used, referring to the table. Provide enough detail so that another student
could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use
the symbols defined in the table and/or include a simple diagram of the setup.
(c) How could the students graphically analyze the data from the procedure in part (b) to determine whether the
relationship of the momentum of the cart –bar system and the momentum of the cart –bar system immediately
after recoil is linear or nonlinear?
(d) Student 1 claims that the interaction between the carts is elastic. Student 2 claims the interaction between the
carts is inelastic. Indicate which student is correct, and why.
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Test Booklet
Experiment Design FRQ
5.
This question is a long free-response question. Show your work for each part of the question.
(
points, suggested time
minutes)
A projectile launcher consists of a spring with an attached plate, as shown in Figure . When the spring is
compressed, the plate can be held in place by a pin at any of three positions , , or . For example, Figure
shows a steel sphere placed against the plate, which is held in place by a pin at position . The sphere is launched
upon release of the pin.
A student hypothesizes that the spring constant of the spring inside the launcher has the same value for different
compression distances.
(a) The student plans to test the hypothesis by launching the sphere using the launcher.
i. State a basic physics principle or law the student could use in designing an experiment to test the hypothesis.
ii. Using the principle or law stated in part (a)(i), determine an expression for the spring constant in terms of
quantities that can be obtained from measurements made with equipment usually found in a school physics
laboratory.
(b) Design an experimental procedure to test the hypothesis in which the student uses the launcher to launch the
sphere. Assume equipment usually found in a school physics laboratory is available.
In the table below, list the quantities and associated symbols that would be measured in your experiment. Also list
the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need
additional rows, you may add them to the space just below the table.
Quantity to be Measured
Symbol for Quantity
Equipment for Measurement
Describe the overall procedure to be used to test the hypothesis that the spring constant of the spring inside the
launcher has the same value for different compression distances, referring to the table. Provide enough detail so
that another student could replicate the experiment, including any steps necessary to reduce experimental
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AP Physics 1
Test Booklet
Experiment Design FRQ
uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup.
(c) Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that the spring
constant of the spring inside the launcher has the same value for different compression distances.
(d) Another student uses the launcher to consecutively launch several spheres that have the same diameter but
different masses, one after another. Each sphere is launched from position . Consider each sphere’s launch
speed, which is the speed of the sphere at the instant it loses contact with the plate. On the axes below, sketch a
graph of launch speed as a function of sphere mass.
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Test Booklet
Experiment Design FRQ
6.
A group of students has two carts, A and B, with wheels that turn with negligible friction. The carts can travel
along a straight horizontal track. Cart A has known mass mA. The students are asked to use a one dimensional
collision between the carts to determine the mass of cart B. Before the collision, cart A travels to the right and cart
B is initially at rest, as shown above. After the collision, the carts stick together.
(a) Describe an experimental procedure to determine the velocities of the carts before and after a collision,
including all the additional equipment you would need. You may include a labeled diagram of your setup to help
in your description. Indicate what measurements you would take and how you would take them. Include enough
detail so that another student could carry out your procedure.
(b) There will be sources of error in the measurements taken in the experiment, both before and after the collision.
For your experimental procedure, will the uncertainty in the calculated value of the mass of cart B be affected
more by the error in the measurements taken before the collision or by those taken after the collision, or will it be
equally affected by both sets of measurements? Justify your answer.
A group of students took measurements for one collision. A graph of the students’ data is shown below.
(c) Given mA = 0.50 kg, use the graph to calculate the mass of cart B. Explicitly indicate the principles used in
your calculations.
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AP Physics 1
Test Booklet
Experiment Design FRQ
(d) The students are now asked to consider the kinetic energy changes in an inelastic collision, specifically
whether the initial values of one of the physical quantities affect the fraction of mechanical energy dissipated in
the collision. How could you modify the experiment to investigate this question? Be sure to explicitly describe the
calculations you would make, specifying all equations you would use (but do not actually do any algebra or
arithmetic).
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Test Booklet
Experiment Design FRQ
7.
A student hangs a 0.125 kg object on a spring, sets it into oscillation, and obtains the data for the position and
velocity of the object as a function of time shown in the graphs below.
(a) On the grid below, sketch the potential energy of the object-spring-Earth system as a function of time.
Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values, as appropriate.
(b) On the axes below, sketch the acceleration of the object as a function of time. Explicitly label any intercepts,
asymptotes, maxima, or minima with numerical values, as appropriate.
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AP Physics 1
Test Booklet
Experiment Design FRQ
Next the student is given a rubber band and asked to determine whether the relationship between the restoring
force exerted by the rubber band and the amount it is stretched is the same as that of an ideal spring.
(c) Describe an experimental procedure that the student could use to collect the necessary data, including all the
equipment the student would need.
(d) How should the student analyze the data to determine whether the relationship between the restoring force
exerted by the rubber band and the amount it is stretched is the same as that of an ideal spring? What evidence
from the analysis would be used to make the determination?
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Test Booklet
Experiment Design FRQ
8.
This question is a long free-response question. Show your work for each part of the question.
(12 points, suggested time 25 minutes)
A group of students is investigating how the thickness of a plastic rod affects the maximum force
with
which the rod can be pulled without breaking. Two students are discussing models to represent how
depends on rod thickness.
Student claims that
is directly proportional to the radius of the rod.
Student claims that
is directly proportional to the cross-sectional area of the rod—the area of the base of
the cylinder, shaded gray in the figure above.
(a) The students have a collection of many rods of the same material. The rods are all the same length but come in
a range of six different thicknesses. Design an experimental procedure to determine which student’s model, if
depends on rod thickness.
either, correctly represents how
In the table below, list the quantities that would be measured in your experiment. Define a symbol to represent
each quantity, and also list the equipment that would be used to measure each quantity. You do not need to fill in
every row. If you need additional rows, you may add them to the space just below the table.
Quantity to be Measured
Symbol for Quantity
Equipment for Measurement
Describe the overall procedure to be used, referring to the table. Provide enough detail so that another student
could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use
the symbols defined in the table and/or include a simple diagram of the setup.
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AP Physics 1
Test Booklet
Experiment Design FRQ
(b) For a rod of radius , it is determined that
is , as indicated by the dot on the grid below. On the grid,
draw and label graphs corresponding to the two students’ models of the dependence of
on rod radius.
Clearly label each graph “ ” or “ ,” corresponding to the appropriate model.
The table below shows results of measurements taken by another group of students for rods of different
thicknesses.
Rod radius (
) 0.5 1.0 1.5 2.0 2.5
40 120 320 520 900
(c) On the grid below, plot the data points from the table. Clearly scale and label all axes, including units. Draw
either a straight line or a curve that best represents the data.
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Test Booklet
Experiment Design FRQ
(d) Which student’s model is more closely represented by the evidence shown in the graph you drew in part (c) ?
____ Student
’s model:
is directly proportional to the radius of the rod.
____ Student
’s model:
is directly proportional to the cross-sectional area of the rod.
Explain your reasoning.
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AP Physics 1
Test Booklet
Experiment Design FRQ
9.
In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy that
initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressed length L0
and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression.
The students repeat the experiment several times, measuring h with objects of various masses taped to the top of
the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each
have negligible mass compared to the top of the toy and the objects taped to it.
(a) Derive an expression for the height h in terms of m, x, k, and fundamental constants.
With the spring compressed a distance x = 0.020 m in each trial, the students obtained the following data for
different values of m.
m (kg)
0.020
0.030
0.040
0.050
0.060
h (m)
0.49
0.34
0.28
0.19
0.18
(b)
i. What quantities should be graphed so that the slope of a best-fit straight line through the data points can
be used to calculate the spring constant k?
ii. Fill in one or both of the blank columns in the table with calculated values of your quantities, including
units.
(c) On the axes below, plot your data and draw a best-fit straight line. Label the axes and indicate the scale.
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Test Booklet
Experiment Design FRQ
(d) Using your best-fit line, calculate the numerical value of the spring constant.
(e) Describe a procedure for measuring the height h in the experiment, given that the toy is only momentarily at
that maximum height.
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AP Physics 1
Test Booklet
Experiment Design FRQ
10.
Directions: This question is a long free-response question. Show your work for each part of the question.
2. (12 points, suggested time 25 minutes)
A heavy lab cart moves with kinetic energy
on a track and collides with a lighter lab cart that is initially
at rest. The carts bounce off each other but the collision is not perfectly elastic, causing the two-cart system to
lose kinetic energy
. A student wonders if the fraction of kinetic energy lost from the two-cart system during
the collision
depends on the speed of the first cart before the collision and plans to perform an
experiment.
(a) The student hypothesizes that a greater fraction of kinetic energy is lost from the system during the collision
when the speed of the first cart is greater.
Briefly state one reason the hypothesis might be correct.
(b) Design an experimental procedure that could be used to test the student’s hypothesis. Assume equipment
usually found in a school physics laboratory is available.
In the table below, list the quantities that would be measured and the equipment that would be used to measure
each quantity. Also, define a symbol to represent each quantity. You do not need to use every row and may add
additional rows as needed.
Quantity to be Measured
Symbol
Equipment for Measurement
Describe the overall procedure to be used, referring to the table above. Provide enough detail so that another
student could replicate the experiment. As needed, use the symbols defined in the table and/or include a simple
diagram of the setup. Be sure to address how experimental uncertainty could be reduced.
(c) Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that a greater
fraction of kinetic energy is lost from the system during the collision when the speed of the first cart is greater.
Include a description or example of any equations, data tables, graphs, or other representations that could be used.
(d) Consider a different scenario in which the carts stick together after the collision. The masses of the heavier and
lighter cart are
and
, respectively. Derive an expression for the fraction of kinetic energy lost
during the collision. Express your answer in terms of
and
.
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Test Booklet
Experiment Design FRQ
11.
This question is a long free-response question. Show your work for each part of the question.
(12 points, suggested time 25 minutes)
A block of mass
can be attached to a parachute of negligible mass and radius , as shown in the two views
above. When falling, the parachute experiences an upward force of air resistance. This force increases as the speed
of the parachute increases. The falling block and parachute speed up at first but eventually reach a constant speed
called terminal speed.
(a) The dot below represents the block-parachute system when it has reached its terminal speed and is falling at
this constant speed. On the dot, draw and label the forces (not components) acting on the system. Represent each
force by a distinct arrow starting on, and pointing away from, the dot.
Note: Draw the relative lengths of all vectors to reflect the relative magnitudes of all the forces.
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AP Physics 1
Test Booklet
Experiment Design FRQ
A group of students has a collection of parachutes of different radii. They are curious about how the terminal
speed depends on the radius of the parachute and find the following equation on the Internet.
,
is the force exerted by air,
where
that has appropriate units.
(b) Determine the units for
The units for
is the parachute’s radius,
is the parachute’s speed, and
is a constant
.
are ________ .
(c)
, derive an equation for the system’s constant terminal speed in terms
i. Based on the above equation for
of , , physical constants, and other relevant quantities that can be measured with equipment usually found in
a school physics laboratory, as appropriate. Assume the mass of the parachute is negligible and that the only
nonnegligible forces acting on a block-parachute system are the block’s weight
and the force of air
.
resistance
ii. Indicate below what quantities could be measured and then graphed to determine whether the equation
derived in part (c)(i) correctly relates the parachute’s radius and the terminal speed of the block-parachute
system.
Vertical axis: __________________
Horizontal axis: __________________
iii. On the axes below, sketch a graph showing the relationship between the two quantities indicated in part
(c)(ii) and based on the equation derived in part (c)(i).
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Test Booklet
Experiment Design FRQ
(d) Design an experimental procedure the students could use to collect the data needed to test whether or not the
relationship between the parachute’s radius and the terminal speed is described by the graph drawn in part (c)(iii).
Assume equipment usually found in a school physics laboratory is available.
In the table below, list the quantities that would be measured in your experiment. Define a symbol to represent
each quantity, and also list the equipment that would be used to measure each quantity. You do not need to fill in
every row. If you need additional rows, you may add them to the space just below the table.
Quantity to be Measured
Symbol for Quantity
Equipment for Measurement
Describe the overall procedure to be used, referring to the table. Provide enough detail so another student could
replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the
symbols defined in the table. Include a simple diagram of the setup. As part of your description, be sure to explain
how the students would know that they are measuring the constant terminal speed.
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AP Physics 1
Test Booklet
Experiment Design FRQ
Diagram of Experimental Setup
Description of Experimental Procedure
(e) In another experiment, the students collect the following data showing the height of a block above the floor at
different times, where the block is dropped from rest at time
with the attached parachute fully open.
Time
Height of Block Above Floor
Use the data shown above to determine the terminal speed of the block.
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Test Booklet
Experiment Design FRQ
12.
An experiment is performed using the apparatus above. A small disk of mass m1 on a frictionless table is attached
to one end of a string. The string passes through a hole in the table and an attached narrow, vertical plastic tube.
An object of mass m2 is hung at the other end of the string. A student holding the tube makes the disk rotate in a
circle of constant radius r, while another student measures the period P.
(a) Derive the equation
that relates P and m2.
The procedure is repeated, and the period P is determined for four different values of m2, where m1 = 0.012 kg and
r = 0.80 m. The data, which are presented below, can be used to compute an experimental value for g.
0.020 0.040 0.060 0.080
P (s)
1.40
1.05
0.80
0.75
(b) What quantities should be graphed to yield a straight line with a slope that could be used to determine g ?
(c) On the grid below, plot the quantities determined in part (b), label the axes, and draw the best-fit line to the
data. You may use the blank rows above to record any values you may need to calculate.
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Test Booklet
Experiment Design FRQ
(d) Use your graph to calculate the experimental value of g.
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