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## Homework Statement

So I am stuck on this homework problem. I understand the general direction I have to take, but my algebra and physics aren't good. Here's the problem:

A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 10.0 m/s at the end of 6.0 s. At that instant, the kinetic energy of the system is 90 J and each mass has moved a distance of 30.0 m. Determine the values of m1 and m2.

## Homework Equations

Wnet = change in KE

total KE of the system = 0.5(m1)v^2 + 0.5(m2)v^2

W = force * distance

## The Attempt at a Solution

My work so far has not really gotten me anywhere, any tips would be very helpful.

First, I saw that the KE of the system would be the KE equation but with m 1 and m 2 , like this: KE = 0.5(m1+m2 )v^2, or 90=0.5(m1+m2 )v^2, or 90=0.5(m1+m2 )100

So then then m1+m2 would be equal to 9/5.

I'm not sure about this next part I've done: The net work is equal to the change in KE. Since the system starts from rest, the initial KE is 0, and the final KE is 90.

So I did: W=0.5(m1+m2 )100. Then using the work equation: FΔX=0.5(m1+m2)100, and since ΔX is equal to 30m: 30F=0.5(m1+m2)100

I tried substituting in the acceleration in order to get the force of the masses, 10/6=5/3m/s/s, so weight 1 = m1*5/3, and weight 2 = m2*5/3.

With these, I know there is supposed to be 2 equations for 2 unknowns, but I can't seem to figure them out. I'm kind of lost at his point.

I've uploaded a picture of the problem. I believe I'm headed in the right direction. Any tips?