# With what magnitude must the man pull on the rope

## Homework Statement

A man is strapped to a chair which is connected to a pulley (combined weight of chair and person = 95 kilograms). With what magnitude must the man pull on the rope if he is to rise

a) with a constant velocity

b) with an upwards velocity of 1.3 meters per seconds squared.

tension = mass X acceleration

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first draw a FBD labelling forces, that will tell you much about the problem

this is what I drew as a Free Body Diagram with the information given:

Tension
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person/chair
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Weight

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Is the pully frictionless?

Doc Al
Mentor
A man is strapped to a chair which is connected to a pulley (combined weight of chair and person = 95 kilograms). With what magnitude must the man pull on the rope if he is to rise
Is the man pulling himself and his chair up and does the rope loop around a pulley attached to the ceiling? (A diagram will help.)

If so, you'll need to revise your free body diagram.

oh sorry for not being more specific :(. the pulley is frictionless, and the man is pulling himself and the chair up via the rope (connected to the chair) that goes through the pulley connected to the ceiling and then falls back down again, allowing the man to grab it and pull himself and the chair up

Doc Al
Mentor
Good. Now revise your free body diagram accordingly. Hint: How many times does the rope pull up on the 'man + chair'?

well in the positive y-direction (up) there is tension and in the negative y- direction there is weight and the force which is caused by the man pulling on the rope in order to life himself up. so would it be the same free body diagram, but with a negative force added to the bottom?

Doc Al
Mentor
Hint: How many times does the rope pull up on the 'man + chair'?
I'll rephrase my question. Draw an imaginary box around the 'man + chair' contraption. How many ropes pass through the boundary of that box?

ohhhh okayyy

then two ropes, one rope connected to the chair, and one rope which the man uses to pull himself and the chair up...would there be two different tensions then?

Doc Al
Mentor
then two ropes, one rope connected to the chair, and one rope which the man uses to pull himself and the chair up...would there be two different tensions then?
Good! There would be two separate tensions acting. (Not necessarily different though.) One end of the rope pulls up on his hands; the other pulls up on his chair. They both count towards the net force on the 'man + chair'.

(Compare this situation to one where the rope attaches to the ceiling without a pulley and thus is not doubled over.)

alright, so then the Net Tension = ((mass x acceleration) + weight) + (mass x acceleration)?

Doc Al
Mentor
alright, so then the Net Tension = ((mass x acceleration) + weight) + (mass x acceleration)?
I find that very confusing.

Instead, just write ΣF = ma. Call the tension in the rope 'T'. What's the net force (ΣF)?

Σf = (t + w) + (t)

sorry, for some reason when I posted it, none of the letter remained capitalized

Doc Al
Mentor
Σf = (t + w) + (t)
What direction do these force have? (Do they all have the same sign?)

well the first tension is positive since it is holding the chair and man up. the weight (w) is negative since it the force working against the tension. I believe the last tension would be negative since it is caused by the man pulling on the rope to pull himself and the chair up.

Doc Al
Mentor
well the first tension is positive since it is holding the chair and man up.
OK. The rope pulls up on the chair, thus is a positive force.
the weight (w) is negative since it the force working against the tension.
The weight acts down, so is negative.
I believe the last tension would be negative since it is caused by the man pulling on the rope to pull himself and the chair up.
All we care about are forces on the man/chair. The rope pulls up on the man and up on the chair. Both tension forces are positive.