Q. 69

Expert-verified
Found in: Page 260

### 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 pendulum is formed from a small ball of mass m on a string of length L. As FIGURE shows, a peg is height above the pendulum’s lowest point. From what minimum angle u must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

Minimum angle

See the step by step solution

## Step 1: Given information

Given a pendulum with a small ball of mass m.

Height of the peg,

## Step 2: Explanation

According to Newton's second law,

At the critical velocity , the tension in the string will tend to

Therefore the equation

According to the energy conservation equation, gravitational potential energy is transformed into the critical kinetic energy of the ball,

That is, the ball is a vertical distance above the peg's location or a distance of

From the above figure, the minimum angle for the ball to go over the top of the peg: