Concept explainers
(a)
The minimum speed with that Jane begins her swing to just make it to another side.
(a)
Answer to Problem 81CP
The minimum speed with that Jane begin her swing to just make it to other side is
Explanation of Solution
Consider the horizontal motion of Jane, as shown in figure (I) Jane moves from initial point to final point on the other side.
Write the expression for the total horizontal distance
Rearrange the above expression.
Simplify the above expression.
Here,
Consider the body-string-earth system as a non-isolated system. Since there is a force acting on the vine in a positive horizontal direction.
Write the equation for conservation of energy.
Here,
Write the equation for the change in potential energy
Simplify the above expression as.
Here,
The height can be calculated as shown in figure (I) from the equilibrium point.
Substitute
As the body moves with an initial speed and final speed of the body is zero.
Write the expression for the change in kinetic energy as.
Since the body moves with an initial speed and final speed of the body is zero. As the final speed of the body is zero than final the kinetic energy becomes zero.
Substitute
Here,
Write the expression for work done by wind as.
Here,
Substitute
Rearrange the above equation.
Simplify the above equation.
Conclusion:
Substitute
Substitute
Thus, the minimum speed with that Jane begins her swing to just make it to the other side is
(b)
The minimum speed with that Jane and Tarzan begin their swing to just make it to the other side.
(b)
Answer to Problem 81CP
The minimum speed with that Jane and Tarzan begin their swing to just make it to other side is
Explanation of Solution
Consider the body-string-earth system as a non-isolated system. Since there is a force acting on the vine in a positive horizontal direction.
The height can be calculated as shown in figure (I) from the equilibrium point.
Substitute
Since the body moves with an initial speed and final speed of the body is zero. As the final speed of the body is zero than final the kinetic energy becomes zero.
Substitute
Here,
Write the expression for work done by wind as.
Here,
Substitute
Rearrange the above equation.
Simplify the above equation.
Since the total mass of the system is the mass of Jane and Tarzan.
Conclusion:
Substitute
Thus, the minimum speed with that Jane and Tarzan begin their swing to just make it to the other side is
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Chapter 8 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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