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Q. 50

Expert-verified
Found in: Page 417

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A mass hanging from a spring oscillates with a period of . Suppose the mass and spring are swung in a horizontal circle, with the free end of the spring at the pivot. What rotation frequency, in rpm, will cause the spring's length to stretch by ?

Rotational frequency in rpm is .

See the step by step solution

## Step 1: Expression for

The period of oscillation of the mass is,

Rearrange it,

## Step 2: Expression for rotation frequency

A radial force acting toward the path's center of curvature is required for the mass to travel in a uniform circular motion.

In this situation, the radial force is the force exerted by the spring on the mass.

The net force on the mass is,

Substitute all values,

## Step 3: Calculation for rotational frequency

Frequency is,

Where ,

converted to rpm,