(a)
The maximum speed of the bob.
(a)

Answer to Problem 21P
The maximum speed of the bob is
Explanation of Solution
The formula to calculate amplitude is,
Here,
Substitute
The formula to calculate angular frequency is,
Here,
Substitute
The formula to calculate maximum speed is,
Substitute
Conclusion:
Therefore, the maximum speed of the bob is
(b)
The maximum acceleration of the bob.
(b)

Answer to Problem 21P
The maximum acceleration of the bob is
Explanation of Solution
The formula to calculate maximum acceleration of the bob is,
Substitute
Conclusion:
Therefore, the maximum acceleration of the bob is
(c)
The maximum restoring force of the bob.
(c)

Answer to Problem 21P
The maximum restoring force of the bob is
Explanation of Solution
The formula to calculate maximum restoring force of the bob is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the maximum restoring force of the bob is
(d)
The maximum speed,
(d)

Answer to Problem 21P
The maximum speed of the bob is
Explanation of Solution
Consider the figure given below.
In triangle
The height of the bob is,
The law of conservation of energy is,
Substitute
Substitute
The formula for the moment of inertia of the pendulum is,
The equation for the conservation of energy is,
Here,
Substitute
Substitute
The force is maximum, when the angle is maximum.
The restoring force is calculated as,
Substitute
Conclusion:
Therefore, the maximum speed of the bob is
(e)
The answers of part (a), part (c) and part (d).
(e)

Explanation of Solution
The restoring force is defined as the force or torque that tends to restore a system to equilibrium after displacement.
The answers are closest but not exactly the same. The angular amplitude of
Conclusion:
Therefore, the answers are closest but not exactly the same.
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Chapter 15 Solutions
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