(a)
The force exerted by T.
(a)
Answer to Problem 66A
The force exerted by T is
Explanation of Solution
Given:
The weight of the Piano is
The distance up to which the piano is raised is
The length of the rope pulled by T is
Formula used:
The efficiency of a machine is the ratio of output work to the input work.
The expression for the efficiency of the machine is
Here,
Calculation:
Consider T tries to lift the Piano up to a distance of
The resistance force exerted by the Piano is
Consider the effort put by T in lifting the piano is denoted by
The length of the rope pulled by T is
The efficiency of the machine is
The force exerted by Tis,
Conclusion:
Therefore, the force exerted by T is
(b)
The force utilized to balance the friction force.
(b)
Answer to Problem 66A
The force utilized to balance the frictional force is
Explanation of Solution
Given:
The weight of the Piano is
The distance up to which the piano is raised is
The length of the rope pulled by T is
The actual effort force exert by T is
Formula used:
For an equilibrium condition, the total force acting on an object is equal to zero.
Calculation:
The actual effort force exerted by T in lifting the Piano is
From part (a), the effort exerted by the T in lifting the Piano is
The force
Conclusion:
Therefore, the force utilized to balance the frictional force is
(c)
The output work.
(c)
Answer to Problem 66A
The output work done is
Explanation of Solution
Given:
The weight of the Piano is
The distance up to which the piano is raised is
The length of the rope pulled by T is
The actual effort force exert by T is
Formula used:
The output work
Calculation:
The displacement of the load is
The resistance force exerted by the Piano is
The output work done for a machine as follows:
Conclusion:
Therefore, the output work done is
(d)
The input work done.
(d)
Answer to Problem 66A
The input work done is
Explanation of Solution
Given:
The weight of the Piano is
The distance up to which the piano is raised is
The length of the rope pulled by T is
The actual effort force exert by T is
Formula used:
The input work
Calculation:
The effort put by T in lifting the piano is
The length of the rope pulled by T is
The input work done for a machine as follows:
Conclusion:
Therefore, the input work done is
(e)
The mechanical advantage of the machine.
(e)
Answer to Problem 66A
The mechanical advantage of the machine is
Explanation of Solution
Given:
The weight of the Piano is
The distance up to which the piano is raised is
The length of the rope pulled by T is
The actual effort force exert by T is
Formula used:
The mechanical advantage of the machine
Calculation:
The effort put by T in lifting the piano is
The resistance force exerted by the Piano is
The mechanical advantage of the machine as follows:
Conclusion:
Therefore, the mechanical advantage of the machine is
Chapter 10 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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