How Does a Pulley System Help Rescue a Cat from a Tree?

[katie beisel]

Homework Statement

A cat is stuck in a tree. You are designated with the job to get it out, yet you do not want to climb the tree, because you may get stuck as well. Instead you set up a pulley system. A rope (consider it massless) runs from the seat you sit on over an ideal pulley and then to your hand. You pull on the loose end of the rope with a force of 348 N. You weigh 612 N and the seat you sit on weighs 16.0 N. (a) What is your acceleration? (b) What force does the seat exert on you?

Homework Equations

F=ma
t - mg = ma

The Attempt at a Solution

ok so i found the mass to be 64.2 kg
the combined force weight is 628 N
i thought the tension would be 348 N but I'm not getting the right answer with that

 

[Doc Al]

i thought the tension would be 348 N but I'm not getting the right answer with that

That is the tension in the rope.

t - mg = ma

Careful here. The rope pulls on the person and on the seat.

(Hint: For part a, treat the person+seat as a single system. What forces act?)

 

[katie beisel]

That is the tension in the rope.Careful here. The rope pulls on the person and on the seat.

(Hint: For part a, treat the person+seat as a single system. What forces act?)

i did that and i got -4.5 but the answer should be 1.06

 

[Doc Al]

i did that and i got -4.5 but the answer should be 1.06

Show what you did. What forces act on "person+seat"?

 

[katie beisel]

Show what you did. What forces act on "person+seat"?

well they have a combined force weight of 628 N so 348 N - 628 N = 64.1 (i messed up the first time)a
which equals -4.3

 

[Doc Al]

well they have a combined force weight of 628 N so 348 N - 628 N = 64.1 (i messed up the first time)a
which equals -4.3

You have an upward force of only 348 N. But how many rope segments pull up on the system?

 

[katie beisel]

You have an upward force of only 348 N. But how many rope segments pull up on the system?

one

 

[Doc Al]

one

Nope. The rope pulls up twice. Once on the person; once on the seat.

 

[katie beisel]

Nope. The rope pulls up twice. Once on the person; once on the seat.

ok doubling the force tension gives me the right answer but I'm confused why that is. I don't understand why it pulls up twice even though its only connected to the chair.

 

[Doc Al]

I don't understand why it pulls up twice even though its only connected to the chair.

Ah, but it's not only connected to the chair. It's also connected to the person, who is pulling up on one end of the rope. (One end connects to the seat; the other end, to the person.)

Try this: Draw an imaginary box around the "person + seat". How many rope segments connect to that box?