Concept explainers
The load in Fig. 4-7 is hanging at rest. Take the ropes to all be vertical and the pulleys to be weightless and frictionless. (a) How many segments of rope support the combination of the lower pulley and load? (b) What is the downward force on the lowest pulley (the “floating” one)? (c) What must be the total upward force exerted on the floating pulley by the two lengths of rope? (d) What is the upward force exerted on the floating pulley by each length of rope supporting it? (e) What is the tension in the rope wound around the two pulleys? (f) How much force is the man exerting? (g) What is the net downward force acting on the uppermost pulley? (h) How much force acts downward on the hook in the ceiling?
(a)
The segments of the rope that support the combination of the lower pulley given inFigure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The weight of the hanging block is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram of the system:
In the above diagram, point
Since the same rope is passing over theupper pulleyand lower pulley, the magnitude of tensionthroughout the rope should be same. Therefore,
Refer to the above diagram and consider the pulley 1. In this case,
Consider the upward forces as positive and the downward forces as negative. Therefore,
Substitute
Conclusion:
Therefore, two segments of the rope support the combination of the lower pulley and load.
(b)
The magnitude of the downward force applied to the lowest pulleyin the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram when
Recall the expression for the first condition of the force’s equilibrium:
Consider the direction of the upward forces is positive and the direction of the downward forces is negative. Therefore,
Substitute
The tension forces of 200 N, acting in the rope, pule the load in upward direction and weight of the
Conclusion:
Therefore, the magnitude of the downward force on the lowest pulley is
(c)
The magnitude of the total upward force exertedon the floating pulley by the two lengths of ropein the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram of the lowermost pulley:
Recall the expression for the first condition of the force equilibrium:
Consider the direction of the upward forces is positive and the direction of the downward forces is negative. Hence,
Substitute
Conclusion:
The magnitude of the total upward force applied on the pulley by the two lengths of the rope is
(d)
The magnitude of the upward force applied on the floating pulley by each length of rope supporting the pulleyin the figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The weight of the person is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram of the lowermost pulley:
Recall the expression for the first condition of the force’s equilibrium:
Consider the direction of the upward forces is positive and the direction of the downward forces is negative. Hence,
Substitute
Conclusion:
The magnitude of the upward force applied on the floating pulley by each length of the rope is
(e)
The magnitude of the tensionin the rope wound around the two pulleysin the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Refer to the diagram drawn in the subpart (a). A single rope is wounded on the both the polis. So, the magnitude of tension should be same throughout the rope. Therefore,
Substitute
Conclusion:
The magnitude of the tension in the rope wound around the pulley is
(f)
The maximum force applied by the man to pull the ropein the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram of the unwound rope, which is in the right side of the upper pulley, when a man exerts a force F to pull the rope.
To observed the schematic diagram of the problem,
The force
Recall the expression for the first condition of the force’s equilibrium:
Consider the direction of the upward forces is positive and the direction of the downward forces is negative. Hence,
Substitute
Conclusion:
The magnitude of the maximum force applied by the man is
(g)
The magnitude of the net downward force acting on the uppermost pulleyin the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Draw the free body diagram of the upper pulley:
Recall the expression for the first condition of the force’s equilibrium:
Consider the direction of the upward forces is positive and the direction of the downward forces is negative. Hence,
Substitute
The net downward force acting on the uppermost pulleyhas the same magnitude as the tension of the rope, which is
Conclusion:
Therefore, the total downward force acting on the upper pulley is
(h)
The maximum force that is acting downward on the hook in the ceilingin the Figure
Answer to Problem 16SP
Solution:
Explanation of Solution
Given data:
The load is
The load is hanging on rest, so there will be no acceleration.
Formula used:
Write the expression for the first condition of the force’s equilibrium:
Here,
Explanation:
Refer to the schematic diagram of the problem from the subpart (a).
The maximum force applied downward on the hook in the ceiling is equal to the same magnitude of the tension
Conclusion:
Therefore, themaximum force applied downward on the hook in the ceilingis
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