Concept explainers
(a)
The expression for
(a)
Answer to Problem 8.82CP
The expression for
Explanation of Solution
Given info: The length of the string is
The diagram is shown below.
Figure I
The formula to calculate the horizontal displacement is,
Here,
The formula to calculate the work done by the wind force is,
Here,
Substitute
The formula to calculate the gravitational potential energy of the ball is,
Here,
From the law of conservation of energy,
Here,
Substitute
Square the above expression on both sides to find
Substitute
Conclusion:
Therefore, the expression for
(b)
The value of
(b)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(c)
The value of
(c)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(d)
The value of
(d)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
In the above expression, the height of the ball is directly proportional to the square of the magnitude of force as the force increases then the height of the ball also increases but in the given case, the value of force is approach to zero then the height of the ball also approach to zero.
Conclusion:
Therefore, the value of
(e)
The value of
(e)
Answer to Problem 8.82CP
The value of
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for
Substitute
Conclusion:
Therefore, the value of
(f)
The equilibrium height of the ball as a function of
(f)
Answer to Problem 8.82CP
The equilibrium height of the ball as a function of
Explanation of Solution
Given info: The length of the string is
The given diagram is shown below.
Figure II
The diagram is shown below.
Figure III
From the figure the equilibrium height of the ball is,
Here,
From the figure II,
Substitute
Substitute
Conclusion:
Therefore, the equilibrium height of the ball as a function of
(g)
The value of equilibrium height of the ball
(g)
Answer to Problem 8.82CP
The value of equilibrium height of the ball
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for equivalent height of the ball in terms of
Substitute
Conclusion:
Therefore, the value of equilibrium height of the ball
(h)
The value of equilibrium height of the ball
(h)
Answer to Problem 8.82CP
The value of equilibrium height of the ball
Explanation of Solution
Given info: The length of the string is
From part (a), the expression for equivalent height of the ball in terms of
Substitute
Conclusion:
Therefore, the value of equilibrium height of the ball
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Chapter 8 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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