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Chapter 15: Q.34 (page 416)

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’s 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?

Short Answer

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Part A

Part B

Step by step solution

01

Part A

At exactly 12:00 noon, how many oscillations will the pendulum have completed

Number of Oscillations = n

n=tϖ2π=4×3600×9.815-0.0124×1102/2πn=1852.5

01

Part 2

Amplitude = 0.780 m

A(t)=Ae-t2τ=1.5×e(-t/2×11000)=1.5×e(-4×60×60÷22000)A(t)=0.780m

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Most popular questions from this chapter

Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x≤R 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 r≤x; there is no net gravitational force from the mass in the spherical shell with r>x.

a Find an expression for the gravitational force on the particle, assuming the object has uniform density. Your expression will be in terms of x,R,m,M, and any necessary constants.

b 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 SHM. Suppose an intrepid astronaut exploring a 150-km-diameter, 3.5×1018kg 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?

The pendulum shown in figure is pulled to a 10° angle on the left side and released.

a. What is the period of this pendulum?

b. What is the pendulum’s maximum angle on the right side?

A block attached to a spring with unknown spring constant oscillates with a period of 2.0s.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.

The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?

A solid sphere of mass Mand radius Ris suspended from a thin rod, as shown in

FIGURECP15.77.The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency fof small angle oscillations.
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