   Chapter 13.5, Problem 13.7QQ

Chapter
Section
Textbook Problem

A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is measured. If the elevator moves with constant velocity, does the period (a) increase, (b) decrease, or (c) remain the same? If the elevator accelerates upward, does the period (a) increase, (b) decrease, or (c) remain the same?

To determine
How the period of a simple pendulum changes when a stationary elevator moves with constant velocity and How the period of a simple pendulum changes when a stationary elevator accelerates upward.

Explanation

Given info: The simple pendulum is hung from the ceiling of an stationary elevator which starts moving with constant velocity.

Explanation:

The period of a simple pendulum which is having a bob of mass m which is suspended by a light string of length L is given by,

T=2πLg

• T is the time period of the simple pendulum
• L is the length of the string which suspend the bob of the pendulum
• g is the free fall acceleration

When the elevator is moving with constant velocity, its acceleration is 0. Hence there is no change in the value of g . Hence the time period of the simple pendulum does not change.

When the elevator is accelerating upward with an acceleration a , the effective value of g increases to g+a , hence according to (1), the time period of the simple pendulum will decrease

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