Physics Lessons & Exams
AP Physics C 2019 Exam Question 1
AP Physics C 2019 Exam Question 2
2. A toy rocket of mass 0.50 kg starts from rest on the ground and is launched upward, experiencing a vertical net force. The rocket’s upward acceleration a for the first 6 seconds is given by the equation a = K - Lt2, where K = 9.0 m/s2 , L = 0.25 m/s4 , and t is the time in seconds. At t = 6.0 s, the fuel is exhausted and the rocket is under the influence of gravity alone. Assume air resistance and the rocket’s change in mass are negligible.
(a) Calculate the magnitude of the net impulse exerted on the rocket from t = 0 to t = 6.0 s.
(b) Calculate the speed of the rocket at t = 6.0 s.
(c) i. Calculate the kinetic energy of the rocket at t = 6.0 s.
ii. Calculate the change in gravitational potential energy of the rocket-Earth system from t = 0 to t = 6.0 s.
(d) Calculate the maximum height reached by the rocket relative to its launching point.
(e) On the axes below, assuming the upward direction to be positive, sketch a graph of the velocity v of the rocket as a function of time t from the time the rocket is launched to the time it returns to the ground.
Ttop represents the time the rocket reaches its maximum height. Explicitly label the maxima with numerical values or algebraic expressions, as appropriate.
AP Physics C 2019 Exam Question 3
3. The rotational inertia of a rolling object may be written in terms of its mass m and radius r as I = bmr2, where b is a numerical value based on the distribution of mass within the rolling object. Students wish to conduct an experiment to determine the value of b for a partially hollowed sphere. The students use a looped track of radius R >> r, as shown in the figure above. The sphere is released from rest a height h above the floor and rolls around the loop.
(a) Derive an expression for the minimum speed of the sphere’s center of mass that will allow the sphere to just pass point A without losing contact with the track. Express your answer in terms of b, m, R, and fundamental constants, as appropriate.
(b) Suppose the sphere is released from rest at some point P and rolls without slipping. Derive an equation for the minimum release height h that will allow the sphere to pass point A without losing contact with the track.
Express your answer in terms of b, m, R, and fundamental constants, as appropriate. The students perform an experiment by determining the minimum release height h for various other objects of radius r and known values of b. They collect the following data.
(c) On the grid below, plot the release height h as a function of b. Clearly scale and label all axes, including units, if appropriate. Draw a straight line that best represents the data.
(d) The students repeat the experiment with the partially hollowed sphere and determine the minimum release height to be 1.16 m. Using the straight line from part (c), determine the value of b for the partially hollowed sphere.
(e) Calculate R, the radius of the loop.
(f) In part (b), the radius r of the rolling sphere was assumed to be much smaller than the radius R of the loop.
If the radius r of the rolling sphere was not negligible, would the value of the minimum release height h be greater, less, or the same?
Justify your answer.
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