Concept explainers
(a)
The stretch in the string when the ball moves in a horizontal circle as compared to when the ball is at rest.
(a)
Answer to Problem 97P
The stretch in the string when the ball moves in a horizontal circle as compared to when the ball is at rest is
Explanation of Solution
The mass of the ball of the tetherball set is
Write the equation of force in y-direction when the ball is hanging straight vertical.
Here,
Write the equation of the force in y-direction when the ball is swinging.
Here,
Write the formula for the young’s modulus.
Here,
Write the equation for the area.
Here,
Substitute equation (I), (II), and (II) in the above equation and re-write to get an expression for
Conclusion:
Substitute
The stretch in the string when the ball moves in a horizontal circle as compared to when the ball is at rest is
(b)
The kinetic energy of the ball.
(b)
Answer to Problem 97P
The kinetic energy of the ball is
Explanation of Solution
The mass of the ball of the tetherball set is
Write the formula for the force in x-direction.
Here,
Re-write the above equation in terms of kinetic energy.
Here,
Re-write the above equation to get an expression for
Write the equation for
Here,
Substitute equation (VII) and (II) in equation (VI).
Conclusion:
Substitute
The kinetic energy of the ball is
(c)
The time taken by a transverse wave pulse to travel the length of the string from the ball to the top of the poll.
(c)
Answer to Problem 97P
The time taken by a transverse wave pulse to travel the length of the string from the ball to the top of the poll is
Explanation of Solution
The mass of the ball of the tetherball set is
Write the formula for the velocity of a wave through a string.
Here,
Write the formula for the linear mass density of the string.
Here,
Substitute equation (X) in equation (IX).
Write the formula for the time taken for a transverse wave to travel the string.
Here,
Substitute equation (XI), (II) and (III) in equation (XII).
Conclusion:
Substitute
The time taken by a transverse wave pulse to travel the length of the string from the ball to the top of the poll is
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