Concept explainers
(a)
The work done on the mass by the tension of the string in one revolution.
(a)
Answer to Problem 79A
Explanation of Solution
Given:
Mass of an object which is used to swing is
Length of the string is
Figure 1
Formula used:
Work done on the mass by the tension of the string in one revolution can be calculated using the equation,
Where,
Calculation:
When a mass moves in a circular path, the centripetal force acting on the mass is directed towards the center of the circle and the motion of the mass is at right angle to the tension of the string. Hence
Substituting the numerical values in equation
Conclusion:
The work done on the mass by the tension of the string in one revolution is
(b)
To explain − whether the answer obtained to part (a) is in agreement with the work-energy theorem.
(b)
Explanation of Solution
Introduction:
Work-energy theorem: It states that the work done by all the forces exerted on a body is equivalent to the variation in kinetic energy of it. That is,
Work done = Final kinetic energy− initial kinetic energy
Mathematically this can be represented as,
Yes. The answer obtained in the part (a) is in agreement with the work - energy theorem. Because the mass rotates with constant kinetic energy. That means initial and final kinetic energy of the rotating mass are equal. And hence the change in kinetic energy of that mass is zero. The mass rotates in a circular path with a continuous speed.
Chapter 11 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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