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Chapter 1: Q9DQ (page 459)

The system shown in Fig. 14.17 is mounted in an elevator. What happens to the period of the motion (does it increase, decrease, or remain the same) if the elevator (a) accelerates upward at5.0m/s2 ; (b) moves upward at a steady 5.0m/s; (c) accelerates downward at 5.0m/s2? Justify your answers.

Short Answer

Expert verified

(a) Accelerates upward at5.0m/s2 is remain the same.

(b) Moves upward at a steady5.0m/s is remain the same.

(c) Accelerates downward at5.0m/s2 is remain the same.

Step by step solution

01

Determine the formula for SHM

The period of a vertical mass-spring system is given by

T=2ττkm

02

Determine the period of motion

The period of a vertical mass-spring system is given by

T=2ττkm

Where kis the spring force constant and m is mass.

Since the motion of the object is affected by the net acceleration of the objectanet=g±a.

Here the period is independent of the acceleration due to gravity. Therefore the period of the motion if the elevator

(a) accelerates upward ata=5.0ms‐2 will remain the same.

(b) moves upward at a steadya=5.0ms‐1 will remain the same.

(c) accelerates downward ata=5.0ms‐2 will remain the same.

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