Question

In the figure a worker lifts a weight by pulling down on a rope with a force $F_vec$ . The upper pulley is attached to the ceiling by a chain,and the lower pulley is attached to the weight by another chain.The weight is lifted at constant speed. Assume that the rope,pulleys, and chains all have negligible weights.

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A) In terms of ,find the tension in the lower chain.
B) In terms of ,find the tension in upper chain.
C) In terms of ,find the magnitude of the force $F_vec$ if the weight is lifted at constant speed.

My prof told me theanswers were:

each chain =w

F = w/2

but how to i arrive at the se solutions

Answer 1

Concepts and reason

The concept required to solve the question is the Newton’s laws.

For the part A, apply the Newton’s third law of equal and opposite force. For the part B, find the individual forces acting on the point of interest to find the tension in the upper chain. For part C, the individual forces acting on the weight will be helpful.

Fundamentals

For the first part, apply the Newton’s third law. It states that for every action, there is always an equal and opposite reaction. It is mathematically given by,

$F = - F$

For the second part, the free body diagram is drawn is as follows:

For the part C, the above diagram is used to find the magnitude of force.

(A)

Newton’s 3^rd law states that for every action, there is always an equal and opposite reaction. Thus, on the lower chain, the force action on it is w in the downward direction.

So, according to the Newton’s 3^rd law, there must be an equal force in the opposite direction. The opposite force balancing the downward force is called as tension in the lower chain.

It is mathematically given by,

$\vec F = \vec T$

Substitute w for F, where w is the weight which acts as force. T is tension.

$w = \vec T$

Thus, the tension in the lower chain is w.

[Part A]

Part A

Part A

(B)

The diagram given above shows the individual forces acting on the upper chain. Here, the force acting on the upper chain is the result of the half force applied by the person and half by the lower chain.

Thus, the force applied by the upper chain will be half of the original one. Thus,

$\frac{w}{2}$ .

Similarly, the force applied by the lower chain is given by,

$\frac{w}{2}$ .

Thus, the total force on the upper chain is given by,

$\frac{w}{2} + \frac{w}{2} = w$

So, force on the upper chain is w.

[Part B]

Part B

Part B

(C)

In the upper pulley, you do not gain any mechanical advantages, however, the lower pulley reduces the required force by1/2.

Thus, the magnitude of the force $\vec F$ if the weight is lifted at constant speed will be $\frac{1}{2}w$ .

[Part C]

Part C

Part C

Ans: Part A

The tension in the lower chain is w.

Part B

The force on the upper chain is w.

Part C

The magnitude of the force $\vec F$ if the weight is lifted at constant speed will be $\frac{1}{2}w$ .