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

• katie beisel
In summary, a cat is stuck in a tree and a person is designated with the job to get it out. The person sets up a pulley system using a rope and an ideal pulley. The person pulls on the end of the rope with a force of 348 N, while they weigh 612 N and the seat they sit on weighs 16.0 N. The combined force weight of the person and the seat is 628 N. To find the acceleration, the person+seat is treated as a single system and the forces acting on it are taken into account, resulting in an upward force of 348 N and a downward force of 628 N. Doubling the tension force gives the correct answer because the rope pulls up twice
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?

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

katie beisel said:
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.

katie beisel said:
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
Doc Al said:
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

katie beisel said:
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
Doc Al said:
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

katie beisel said:
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?

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

katie beisel said:
one
Nope. The rope pulls up twice. Once on the person; once on the seat.

katie beisel
Doc Al said:
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.

katie beisel said:
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?

## 1. What is tension?

Tension is the force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends.

## 2. How is tension related to acceleration?

In physics, tension is closely related to acceleration through Newton's Second Law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This means that the greater the tension, the greater the acceleration of the object.

## 3. What role does a pulley play in a tension system?

A pulley is a simple machine that helps to redirect the direction of a force and reduce the amount of force needed to lift an object. In a tension system, a pulley can be used to change the direction of the tension force and allow for easier movement of objects.

## 4. How is tension affected by the number of pulleys in a system?

The more pulleys in a system, the less tension is needed to lift an object. This is because each additional pulley reduces the amount of force needed by half. So, with two pulleys, half the force is needed; with three pulleys, one-third of the force is needed, and so on.

## 5. Can tension be negative?

No, tension cannot be negative. It is a force that always acts in the direction of the string or rope and cannot pull in the opposite direction. However, tension can be zero if there are no forces acting on the string or rope.

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