Physics Lessons & Exams
AP Physics C 2019 Exam Question 1
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 θMAX 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 FT 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 θMAX 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 IP 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 ωP after time Δt . During time Δt , the wheel stays in contact with the platform without slipping.
(a) Derive an expression for the angular speed ωP of the platform. Express your answer in terms of IP , r, D, F, Δt , and physical constants, as appropriate.
(b) Determine an expression for the kinetic energy of the platform at the moment it reaches angular speed ωP . Express your answer in terms of IP, r, D, F, Δt , and physical constants, as appropriate.
(c) Derive an expression for the angular speed of the wheel ωW when the platform has reached angular speed ωP . Express your answer in terms of D, r, ωP , and physical constants, as appropriate.
When the platform is spinning at angular speed ωP , 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 IP 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 ωf .
(d) Derive an expression for ωf . Express your answer in terms of ωP , IP , and physical constants, as appropriate. A student now uses the rotating platform (IP = 3.1 kg·m2 ) to determine the rotational inertia IU 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 ωi 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 ωf . Trials are repeated for different values of ωi . A graph of ωf as a function of ωi 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 IU 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 Ki . The total kinetic energy of the platform-object system when it reaches angular speed ωf is K f . Which of the following expressions is true? ____ Kj < Ki ____ Kf = Ki ____ Kf > 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 IU 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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