Concept explainers
(a)
The mass M in terms of m, g , and
(a)
Answer to Problem 88AP
The mass M in terms of m, g , and
Explanation of Solution
The system is in equilibrium, so force on either sides of the pulley must be the same.
Write the expression for the equilibrium.
Here,
Conclusion:
Simplify the above equation.
Therefore, the mass M in terms of m, g, and
(b)
The tension
(b)
Answer to Problem 88AP
The tension
Explanation of Solution
Below figure shows the forces and tension acting on the string.
From the figure,
From the figure,
Conclusion:
Therefore, the tension
(c)
The acceleration of each object
(c)
Answer to Problem 88AP
The acceleration of each object is
Explanation of Solution
Below figure shows the forces and tension acting on the string.
Use Newton’s second law to write the expression for tension
Use Newton’s second law to write the expression for tension
Substitute
Use Newton’s second law to write the expression for tension
Conclusion:
Substitute equation (I) and (II) in (III) and simplify.
All the objects are connected to a single string and hence they have same acceleration.
Therefore, the acceleration of each object is
(d)
The tension
(d)
Answer to Problem 88AP
The tension
Explanation of Solution
Rewrite (I).
Rewrite (II).
Conclusion:
Substitute
Substitute
Therefore, the tension
(e)
The maximum value of
(e)
Answer to Problem 88AP
The maximum value of
Explanation of Solution
Below figure shows the forces acting on the system (including frictional force).
From the figure
Write the expression for friction force acting on
Here,
Write the expression for friction force acting on
Write the expression for tension
The system is in equilibrium,
Substitute 0 for
Similarly, Write the expression for tension
Substitute 0 for
Write the expression for
Substitute 0 for
Substitute
Conclusion:
Equate (V) and (VII).
Therefore, the maximum value of
(f)
The minimum value of
(f)
Answer to Problem 88AP
The minimum value of
Explanation of Solution
For minimum value of
Below figure shows the forces acting on the system (including frictional force).
Therefore,
Conclusion:
Equate both the above expression for
Therefore, the minimum value of
(g)
Comparison the values of
(g)
Answer to Problem 88AP
Comparison the values of
Explanation of Solution
Compare (IX) and (VIII).
Conclusion:
Therefore, the Comparison of the values of
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Chapter 5 Solutions
Physics for Scientists and Engineers With Modern Physics
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