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Chapter 15: Q.19 (page 415)
A student is bouncing on a trampoline. At her highest point, her feet are above the trampoline. When she lands, the trampoline sagsbefore propelling her back up. For how long is she in contact with the trampoline?
She is in contact with the trampoline for
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A block attached to a spring with unknown spring constant oscillates with a period of .What is the period if
a. The mass is doubled?
b. The mass is halved?
c. The amplitude is doubled?
d. The spring constant is doubled? Parts a to d are independent questions, each referring to the initial situation.
In a science museum, a 110 kg brass pendulum bob swings at the end of a 15.0-m-long wire. The pendulum is started at exactly 8:00 a.m. every morning by pulling it 1.5 m to the side and releasing it. Because of its compact shape and smooth surface, the pendulum鈥檚 damping constant is only 0.010 kg/s. At exactly 12:00 noon, how many oscillations will the pendulum have completed and what is its amplitude?
Suppose a large spherical object, such as a planet, with radius and mass has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius ; there is no net gravitational force from the mass in the spherical shell with .
. Find an expression for the gravitational force on the particle, assuming the object has uniform density. Your expression will be in terms of , , , , and any necessary constants.
. You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with . Suppose an intrepid astronaut exploring a -km-diameter, kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through the asteroid and emerge on the other side?
A molecular bond can be modeled as a spring between two
atoms that vibrate with simple harmonic motion. FIGURE P15.63
shows an SHM approximation for the potential energy of an HCl
molecule. Because the chlorine atom is so much more massive
than the hydrogen atom, it is reasonable to assume that the hydrogen
atom vibrates back and forth while
the chlorine atom remains at rest. Use the graph to estimate the
vibrational frequency of the HCl molecule.
A air-track glider is attached to a spring. The glider is pushed in 10 cm .and released. A student with a stopwatch finds that oscillations take 12.0 s . What is the spring constant?
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