【AP物理C】【真题】解答题2008力学
?AP Physics C: Mechanics
2008 Free-Response Questions
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PHYSICS C: MECHANICS
SECTION II
Time-45 minutes
3 Questions
Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the
questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all
your work in the pink booklet in the spaces provided after each part, NOT in this green insert.
2008M1. A skier of mass M is skiing down a frictionless hill that makes an angle , with the horizontal, as shown in the diagram. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F = –bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in termsM, b, of ,, and fundamental constants.
(a) On the dot below that represents the skier, draw a free-body diagram indicating and labeling all of the
forces that act on the skier while the skier descends the hill.
(b) Write a differential equation that can be used to solve for the velocity of the skier as a function of
time.
(c) Determine an expression for the terminal velocity of the skierv. T
(d) Solve the differential equation in part (b) to determine the velocity of the skier as a function of time,
showing all your steps .
(e) On the axes below, sketch a graph of the acceleration a of the skier as a function of time t, and indicate
the initial value of a. Take downhill as positive.
a
O
t
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2008M2. The horizontal uniform rod shown above has length 0.60 m and mass 2.0 kg. The left end of the rod is
attached to a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is supported by a cord that makes an angle of 30? with the rod. A spring scale of negligible mass measures the tension in the cord. A 0.50 kg block is also attached to the right end of the rod.
(a) On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force
vector originating at its point of application.
(b) Calculate the reading on the spring scale.
12ML(c) The rotational inertia of a rod about its center is , where M is the mass of the rod and L is its length. 12
Calculate the rotational inertia of the rod-block system about the hinge.
(d) If the cord that supports the rod is cut near the end of the rod, calculate the initial angular acceleration of the
rod-block system about the hinge.
2008M3. In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hang in equilibrium and then measures the entire length of the cord. The data are recorded in the table below:
Weight (N) 0 10 15 20 25
Length (m) 0.60 0.97 1.24 1.37 1.64
(a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through
the data.
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(b) Use the best-fit line you sketched in part (a) to determine an experimental value for the sprink of g constant the cord.
The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at which the top of the cord is tied to the rod, as represented above. When the object is released from rest, it falls 1.5 m before stopping and turning around. Assume that air resistance is negligible. (c) Calculate the value of the unknown mass m of the object.
(d) i. Calculate how far down the object has fallen at the moment it attains its maximum speed.
ii. Explain why this is the point at which the object has its maximum speed.
iii. Calculate the maximum speed of the object.
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