   Chapter 13, Problem 55P

Chapter
Section
Textbook Problem

A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform string of mass 0.060 0 kg and length L. If the period of oscillation of the pendulum is 2.00 s, determine the speed of a transverse wave in the string when the pendulum hangs vertically.

To determine

The speed of a transverse wave in the string when the pendulum hangs vertically.

Explanation

Given info: The mass of the ball is 5.00kg. The mass of the string is 0.0600kg. Length of the string is L. The period of the oscillation is 2.00s.

The period of the pendulum is given by,

T=2πLg

Solve for the length of the string,

L=gT24π2

Substitute 2.00s for T and 9.80ms-2 for g to find L.

L=(9.80ms-2)(2.00s)24π2=0.993m

The linear density of the string,

μ=mL

Substitute 0.0600kg for m and 0.993 m for L to find μ.

μ=0.0600kg0.993m=6.04×102kgm-1

The tension on the string will be,

F=mballg

• mball is the mass of the ball

Substitute 9

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