AP Physics C 2019 Exam Questions Set 1 (pdf)

Corrections for Q2 Solutions:- Tension should equal 9Mg
- For theta_max, it should be 1/18 instead of 1/6.

AP Physics C 2019 Exam Question 1

- In an experiment, students used video analysis to track the motion of an object falling vertically through a fluid
in a glass cylinder. The object of m = 12 g is released from rest at the top of the column of fluid, as shown above.

The data for the speed v of the falling object as a function of time t are graphed on the grid below. The dashed curve represents the best fit chosen by the students for these data.

(a) i. Does the speed of the object increase, decrease, or remain the same?

____ Increase ____ Decrease ____ Remain the same

ii. In a brief statement, describe the direction of the object’s acceleration and how the magnitude of this acceleration changed as the object fell.

iii. Using the graph, calculate an approximate value for the magnitude of the acceleration of the object at t = 0.20 s.

The students use the equation v = A(1 − e^{−Bt}) to model the speed of the falling object and find the best fit coefficients to be A = 1.18 m/s and B = 5 s^{-1}.

(b) Use the above equation to:

i. Derive an expression for the magnitude of the vertical displacement y(t) of the falling object as a function of time t .

ii. Derive an expression for the magnitude of the net force F t( ) exerted on the object as it falls through the fluid as a function of time t .

The students repeat the experiment with a taller glass cylinder that is filled with the same fluid. The cylinder is tall enough so that the object reaches a constant speed.

(c) i. Determine the constant speed of the object.

Justify your answer.

ii. Determine the force exerted by the fluid on the object at this time.

Justify your answer.

AP Physics C 2019 Exam Question 2

2. A pendulum of length L consists of block 1 of mass 3M attached to the end of a string. Block 1 is released
from rest with the string horizontal, as shown above. At the bottom of its swing, block 1 collides with block 2 of
mass M, which is initially at rest at the edge of a table of height 2L. Block 1 never touches the table. As a result
of the collision, block 2 is launched horizontally from the table, landing on the floor a distance 4L from the base
of the table. After the collision, block 1 continues forward and swings up. At its highest point, the string makes
an angle θ_{MAX} to the vertical. Air resistance and friction are negligible. Express all algebraic answers in terms of
M, L, and physical constants, as appropriate.

(a) Determine the speed of block 1 at the bottom of its swing just before it makes contact with block 2.

(b) On the dot below, which represents block 1, draw and label the forces (not components) that act on block 1
just before it makes contact with block 2. Each force must be represented by a distinct arrow starting on, and
pointing away from, the dot. Forces with greater magnitude should be represented by longer vectors.

(c) Derive an expression for the tension F_{T} in the string when the string is vertical just before block 1 makes
contact with block 2. If you need to draw anything other than what you have shown in part (b) to assist in
your solution, use the space below. Do NOT add anything to the figure in part (b).

For parts (d)–(g), the value for the length of the pendulum is L = 75 cm.

(d) Calculate the time between the instant block 2 leaves the table and the instant it first contacts the floor.

(e) Calculate the speed of block 2 as it leaves the table.

(f) Calculate the speed of block 1 just after it collides with block 2.

(g) Calculate the angle θ_{MAX} that the string makes with the vertical, as shown in the original figure, when
block 1 is at its highest point after the collision.

AP Physics C 2019 Exam Question 3

3. A horizontal circular platform with rotational inertia I_{P} rotates freely without friction on a vertical axis. A small
motor-driven wheel that is used to rotate the platform is mounted under the platform and touches it. The wheel
has radius r and touches the platform a distance D from the vertical axis of the platform, as shown above. The
platform starts at rest, and the wheel exerts a constant horizontal force of magnitude F tangent to the wheel until
the platform reaches an angular speed ω_{P} after time Δ_{t} . During time Δ_{t} , the wheel stays in contact with the
platform without slipping.

(a) Derive an expression for the angular speed ω_{P} of the platform. Express your answer in terms of I_{P} , r, D, F,
Δ_{t} , and physical constants, as appropriate.

(b) Determine an expression for the kinetic energy of the platform at the moment it reaches angular speed ω_{P} .
Express your answer in terms of I_{P}, r, D, F, Δ_{t} , and physical constants, as appropriate.

(c) Derive an expression for the angular speed of the wheel ω_{W} when the platform has reached angular
speed ω_{P} . Express your answer in terms of D, r, ω_{P} , and physical constants, as appropriate.

When the platform is spinning at angular speed ω_{P} , the motor-driven wheel is removed. A student holds a disk
directly above and concentric with the platform, as shown above. The disk has the same rotational inertia I_{P} as
the platform. The student releases the disk from rest, and the disk falls onto the platform. After a short time, the
disk and platform are observed to be rotating together at angular speed ω_{f} .

(d) Derive an expression for ω_{f} . Express your answer in terms of ω_{P} , I_{P} , and physical constants, as
appropriate.
A student now uses the rotating platform (IP = 3.1 kg·m^{2} ) to determine the rotational inertia I_{U} of an
unknown object about a vertical axis that passes through the object’s center of mass. The platform is rotating at
an initial angular speed ω_{i} when the unknown object is dropped with its center of mass directly above the center
of the platform. The platform and object are observed to be rotating together at angular speed ω_{f} . Trials are
repeated for different values of ω_{i} . A graph of ω_{f} as a function of ω_{i} is shown on the axes below.

(e)
i. On the graph on the previous page, draw a best-fit line for the data.
ii. Using the straight line, calculate the rotational inertia of the unknown object I_{U} about a vertical axis
passing through its center of mass.

(f) The kinetic energy of the spinning platform before the object is dropped on it is K_{i} . The total kinetic energy
of the platform-object system when it reaches angular speed ω_{f} is K f . Which of the following
expressions is true?
____ K_{j} < K_{i} ____ K_{f} = K_{i} ____ K_{f} > K _{i}

Justify your answer.

(g) One of the students observes that the center of mass of the object is not actually aligned with the axis of
the platform. Is the experimental value of I_{U} obtained in part (e) greater than, less than, or equal to the
actual value of the rotational inertia of the unknown object about a vertical axis that passes through its
center of mass?

____ Greater than ____ Less than ____ Equal to

Justify your answer.

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