Physics 2
Chapter 13 problems
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13.15 Weighing Astronauts This procedure has actually bben used to
“weigh” astronauts in space. A 42.5kg chair is attached to a spring and allowed
to oscillate. When it is empty, the chair takes 1.3s to make one complete
vibration. But with an astronaut sitting in it, with her feet off the floor, the chair
takes 2.54s for one cycle. What is the mass of the astronaut?
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13.27 You are watching an object that is moving in SHM. When the object is
displaced 0.6m to the right of its equilibrium position, it has a velocity of 2.2m/s
to the right and an acceleration of 8.4m/s to the left. How much farther from
this point will the object move before it stops momentarily and then starts to
move back to the left?
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13.52 A 1.8kg monkey wrench is pivoted 0.25m from its center of mass and
allowed to swing as a physical pendulum. The period for small-angle oscillations
is 0.94s.
(a) What is the moment of inertia of the wrench about an axis through the pivot?
(b) If the wrench is initially displaced 0.4 radians from its equilibrium position,
what is the angular speed of the wrench as it passes through the equilibrium
position?
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13.65 A glider is oscillating in SHM on an air track with an amplitude A1. You
slow it so that its amplitude is halved. What happens to its
(a) period, frequency and angular frequency;
(b) total mechanical energy;
(c) maximum speed;
(d) speed at x=A1/4;
(e) potential and kinetic energies at x=A1/4?
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13.68 A block with mass M rests on a frictionless surface and is connected to a
horizontal spring of force constant k. The other end of the spring is attached to a
wall. A second block with mass m rests on top of the first block. The coefficient
of static friction between the blocks is s. Find the maximum amplitude of
oscillation such that the top block will not slip on the bottom block.
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13.78 A uniform beam is suspended horizontally by two identical vertical
springs that are attached between the ceiling and each end of the beam. The
beam has mass 225kg, and a 175kg sack of gravel sits on the middle of it. The
beam is oscillating in SHM, with an amplitude of 40cm and a frequency of 0.6 Hz.
(a) The sack of gravel falls off the beam when the beam has its maximum
upward displacement. What are the frequency and amplitude of the
subsequent SHM of the beam?
(b) If the gravel instead falls off when the beam has its maximum speed, what
are the frequency and amplitude of the subsequent SHM of the beam?
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13.78 continued
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13.78 continued
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13.89 In the figure, the upper ball is released from rest, collides with the
stationary lower ball, and sticks to it. The strings are both 50cm long. The
upper ball has mss 2kg, and it is initially 10cm higher than the lower ball, which
has mass 3kg. Find the frequency and maximum angular displacement of the
motion after the collision.
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