# Homework Help: Person in bucket pulling on rope

1. Oct 1, 2011

### matermultorum

1. I don’t have a diagram to add, but it is a simple system.

1 pulley at the top. On the left is a bucket with a person in it. On the right the rope hangs and the person(in the bucket) is pulling down on the rope with unknown force. The system is moving at constant velocity.

Problem: A person pulls himself up using a bucket and pulley apparatus. How hard must he pull downward on the right to lift himself and the bucket on the left? Mass of bucket/person is 65kg.

2. 2T=mg 2T=65(9.8) T=318.5N

3. Intuitively and from the answer key,I know the answer. I know that the up and down forces are equal because the acceleration is zero. What I don’t know how to draw the free body diagram or how to explain it. There is only one free body diagram, correct? That of the bucket/person?
What are the forces acting on the bucket/person? Here are the two options that get the right answer. Does either one shows correct thinking (I won’t be surprised to find that neither do). Can you help me get the explanations corrected?

FIRST TRY-Forces acting on the bucket/person
Up :Tension in rope T

Down: mg-T directed down because when the person pulls it lessens their weight by the amount of the pull

SECOND TRY-Forces acting on the bucket/person
Up: twice the tension in the rope because there is one pulley and the force going down from the pulley also acts up on the rope on the bucket side

Down: mg

Thank you,
matermultorum

Last edited: Oct 1, 2011
2. Oct 1, 2011

### ehild

There is one free-body diagram for any body in the system. It can be the person with the bucket, or the pulley, or the bucket itself or the ceiling...This case it is the bucket with the person.
Draw a picture to the problems. It is easy, helps you to understand the problem and show the people what you think.

The weight is weight , the tension in a rope does not change the gravitational pull of Earth.

That is correct.

ehild

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3. Oct 1, 2011

### matermultorum

Thank you!

Is there a better way to word my explanation?

"twice the tension in the rope because there is one pulley and the force going down from the pulley also acts up on the rope on the bucket side"

4. Oct 1, 2011

### ehild

The force does not "go down from the pulley". The pulley acts on the rope, and the man and the bucket also act on the rope, and the result is some tension in the rope which is the same all along the rope this time. The rope acts at its both ends, with the same force on the bucket/man.

Always draw the forces starting from the object you investigate. Add the forces which act on the same object.
It is enough to say that the tension in the rope acts at both ends on the object with upward forces T, and gravity G acts downward. The resultant force is 2T-G, and as the object moves with constant velocity, the resultant force is zero, that is T=mg/2. The rope pulls the hand of man with mg/2 force upward, so the man has to pull the rope with the same force downward.

ehild