Concept explainers
(a)
The maximum height of the ball using conservation of energy.
(a)
Answer to Problem 74PQ
The maximum height of the ball is
Explanation of Solution
Write the expression for the conservation of energy for the situation.
Here,
Assume that the gravitational potential energy is zero on Mimas’s surface. The kinetic energy of the ball will be zero at the maximum height.
Write the expression for
Write the expression for
Here,
Write the expression for
Here,
Put equations (II) to (IV) in equation (I) and rewrite it for
Conclusion:
It is given that the speed of the ball is
Substitute
Therefore, the maximum height of the ball is
(b)
The maximum height of the ball using universal gravitation.
(b)
Answer to Problem 74PQ
The maximum height of the ball using universal gravitation is
Explanation of Solution
Write the equation for the initial gravitational potential energy of the ball using universal gravitation.
Here,
Write the equation for the gravitational potential energy of the ball at maximum height using universal gravitation.
Here,
The final kinetic energy of the ball is zero.
Put equations (III), (VI), (VII) and (VIII) in equation (I) and rewrite it for
Write the expression for the height of the ball above the surface of Mimas.
Conclusion:
Given that the value of
Substitute
Substitute
Therefore, the maximum height of the ball using universal gravitation is
(c)
The difference in result of part (a) with that of part (b) as percent and whether the estimate is too high or low.
(c)
Answer to Problem 74PQ
The percent difference of estimate of part (a) with the result of part (b) is
Explanation of Solution
The value obtained for
Calculate the percent difference between the two values.
Conclusion:
The result obtained in part (a) is lower than the more accurate value in part (b) by
Therefore, the percent difference of estimate of part (a) with the result of part (b) is
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Chapter 8 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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