Concept explainers
(a)
The minimum speed of the swing with which Jane must begin her swing to just make it to the other side.
(a)
Answer to Problem 8.81CP
The minimum speed of the swing with which Jane must begin her swing to just make it to the other side is
Explanation of Solution
Given info: The mass of Jane is
The diagram is shown below.
Figure I
From the figure, the width of the river is,
Here,
Rearrange the above formula for
Substitute
Thus, the value of
The formula to calculate the initial kinetic energy of Jane is,
Here,
Thus, the initial kinetic energy of Jane is
The formula to calculate the final kinetic energy of Jane is,
Here,
Substitute
Thus, the final kinetic energy of the Jane is
The formula to calculate the initial gravitational potential energy is,
Here,
Thus, the initial gravitational potential energy is
The formula to calculate the final gravitational potential energy is,
Here,
Thus the final potential energy of the car is
The formula to calculate the initial work done of the wind due to constant force is,
Here,
Substitute
Thus, the initial work done of the wind is
The formula to calculate the law of conservation of energy to the total system is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the minimum speed of the swing that must Jane begin her swing to just make it to the other side is
(b)
The minimum speed of the swing at the beginning.
(b)
Answer to Problem 8.81CP
The minimum speed of the swing at the beginning is
Explanation of Solution
Given info: The mass of Jane is
The formula to calculate the combined mass is,
Here,
Substitute
The formula to calculate the initial kinetic energy is,
Here,
Thus, the initial kinetic energy is
The formula to calculate the final kinetic energy of Jane is,
Here,
Substitute
Thus, the final kinetic energy is
The formula to calculate the initial gravitational potential energy is,
Here,
Thus, the initial gravitational potential energy is
The formula to calculate the final gravitational potential energy is,
Here,
Thus the final potential energy of the car is
The formula to calculate the initial work done of the wind due to constant force is,
Here,
Substitute
Thus, the initial work done of the wind is
The formula to calculate the law of conservation of energy to the total system is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the minimum speed of the swing at the beginning is
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Chapter 8 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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