# Atwood Machine

1. Sep 29, 2015

### JoshW

1. The problem statement, all variables and given/known data

it is Problem 3.30.
2. Relevant equations
I am not sure how to sum the forces about each consecutive pulley I have been at this for 4 hours now. It is sad I can solve the DE questions and not this.

3. The attempt at a solution
I had the first pulley at the top as (where y is dv/dt)
-T+mg=my1

Then I figured if i did it with just one extra pulley I could model the rest how ever it is not correct.

-2T+mg=-my2 (as i set the up direction to be negative and this mass would go up)

Then with two pulleys with the string under it I had either

-3T+mg=-ma or -4T+mg=-my2

What I don't get is how the tension from each consecutive pulley connected to the center of the one above it will effect the system.

2. Sep 29, 2015

### JoshW

3. Sep 30, 2015

### haruspex

The curve of the page makes the end of one line (the number of pulleys) illegible.

Just consider one of the pulleys with the string passing beneath it. If the tension in the string going up from its right is Tn, what is the tension in the string going up from its left hand side? What is the tension in the string going down from its centre?

4. Sep 30, 2015

### JoshW

it says consider N pulleys. so the tension of the one come out of the center would be the sum of the two above it? then string to the left would be just T?

5. Oct 1, 2015

### haruspex

Right. So let the tension in the string passing under the nth pulley be Tn. What is the relationship between Tn and Tn+1?