Concept explainers
(a)
The speed of the bob.
(a)
Explanation of Solution
Introduction:
In the simple pendulum, there is the bob that has mass and is hanged from the string that has the certain length. When the bob is displaced from the equilibrium position the string follows forth and the back motion which is known as the periodic motion.
Write the expression to relate the speed of the bob with the angular speed.
Here,
Write the expression for the angular position with respect to time.
Here,
Differentiate the above equation with respect to time.
Substitute
Write the expression for the velocity.
Here, is the maximum velocity.
Equate equation (2) and (3) for
Solve the above equation for
Write the expression for the angular velocity.
Here,
Substitute
Conclusion:
Thus, the speed of the bob is
(b)
The speed of the bob.
(b)
Explanation of Solution
Introduction:
In the simple pendulum, there is the bob that has mass and is hanged from the string that has the certain length. When the bob is displaced from the equilibrium position the string follows forth and the back motion which is known as the periodic motion.
Write the expression for the conservation for the energy.
Here,
The initial kinetic energy and final potential energy are zero.
Substitute
Write the expression for the kinetic energy.
Here,
Write the expression for the potential energy.
Substitute
Write the expression for the height.
Substitute
Solve the above equation for
Conclusion:
Thus, the speed of the bob is
(c)
The speed of the bob.
(c)
Explanation of Solution
Introduction:
In the simple pendulum, there is the bob that has mass and is hanged from the string that has the certain length. When the bob is displaced from the equilibrium position the string follows forth and the back motion which is known as the periodic motion.
Write the expression for the velocity.
Write the expression for the small angle.
Substitute
Conclusion:
Thus, the speed of the bob is
(d)
The difference in the speeds of the bob.
(d)
Explanation of Solution
Given:
The length is
The angle is
Formula used:
Write the expression for the change in velocity.
Substitute
Calculation:
Substitute
Conclusion:
Thus, the difference in the speed of the bob is
(e)
The difference in the speed of the bob.
(e)
Explanation of Solution
Given:
The length is
The angle is
Formula used:
Write the expression for the change in velocity.
Substitute
Calculation:
Substitute
Conclusion:
Thus, the difference in the velocity of the bob is
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Chapter 14 Solutions
Physics for Scientists and Engineers
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