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Q. 57

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 418

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Short Answer

The pendulum shown in figure is pulled to a 10° angle on the left side and released.

a. What is the period of this pendulum?

b. What is the pendulum’s maximum angle on the right side?

a. The time period of the pendulum is

b. The pendulum's maximum angle on the right side is

See the step by step solution

Step by Step Solution

Step 1: Part (a) Given information

The pendulum is pulled to a angle on the left side and released. So, when we calculating the time period we have to sum up the two time periods of the two ends of pendulum of length .

The time period of the pendulum written as

Where,

L is the length of the pendulum and

g is the acceleration due to gravity.

Step 2: Explanation Part (a) 

Given

The total time period is equal to the sum of periods of two ends of the pendulum

Therefore,

Step 3:  Given information Part (b) 

The pendulum pulled to a angle on the left side. We have to find the pendulum maximum angle at the right side.

For that we have to use the formula of conservation of energy of simple pendulum. Where, as a pendulum swings, its potential energy changes to kinetic energy, then back to potential energy, then back to kinetic energy.

Therefore, the equation of conservation of energy

where is the length of the pendulum

Step 4: Explanation Part (b)

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