Q. 69

Expert-verifiedFound in: Page 260

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

Given a pendulum with a small ball of mass *m.*

Height of the peg,

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:

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