Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 11, Problem 34P
To determine

To Derive: The formula for maximum speed of pendulum.

Expert Solution & Answer
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Answer to Problem 34P

The formula for maximum speed of a simple pendulum bob in relation with gravity, length and angle is vmax = 2×g×L×(1 - cos θ) .

Explanation of Solution

Given info:

Gravity = g

Length = l

Angle of swing=  θ

Formula used:

The expression for law of conservation of energy.

  Etop = Ebottom

This can be written as:

  KEtop + Ubottom = KEtop + Ubottom

Here, KE defines the kinetic energy and U defines the potential energy.

Calculation:

Relate the energy conservation principle to the potential energy at the maximum height of the pendulum to the kinetic energy at the lowest point of the swing. Relating the energy at top kinetic energy is zero and at bottom potential energy is zero is obtained.

  KEtop + Ubottom = KEtop + Ubottom

Substitute the values in the above expressions.

  0 + m×g×h = 12×m×vmax2 + 0 vmax2 = 2×g×hvmax = 2×g×hbut h = L - Lcos θvmax = 2×g×(L - Lcos θ)vmax = 2×g×L (1 - cos θ)

Conclusion:

Thus, the formula for maximum speed of a simple pendulum bob in relation with gravity, length and angle is vmax = 2×g×L×(1 - cos θ) .

Chapter 11 Solutions

Physics: Principles with Applications

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