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Chapter 1: Q11DQ (page 459)

A simple pendulum is mounted in an elevator. Whathappens to the time period of the pendulum (does it increase, decrease,or remain the same) if the elevator

(a) accelerates upward ata=5.0m/s2

(b) moves upward at a steadyv=5.0m/s

(c) acceleratesdownward ata=5.0m/s2

(d) accelerates downward ata=9.8m/s2

Justify your answers.

Short Answer

Expert verified
  1. T will decrease.
  2. T will remain same.
  3. T will increase.
  4. T will be infinity.

Step by step solution

01

Definition of time period of a vertical mass-spring

Time period of a vertical mass-spring is given by

T=2πLgnet

Where L is the length of the pendulum and gnetis the net acceleration due to gravity.

Since, the motion of the object is affected by the net acceleration of the objects i.e.gnet=g±a

Consider downward g as positive.

02

Calculation when acceleration is upwards

(a) Whena=5.0m/s2 we have,

gnet=g+a

Hence, the time period T will decrease.

(b) Whenv=5.0m/s we have,

gnet=g

Hence, the time period T will remain same.

03

Calculation when acceleration is downwards

(c) Whena=5.0m/s2 we have,

gnet=g-a

Hence, the time period T will increase.

(d) Whena=9.8m/s2 we have,

gnet=g-a

Hence, the time period T be infinity.

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