# Homework Help: Conservation of Energy of a System

1. Nov 28, 2014

### Clementine

1. The problem statement, all variables and given/known data:
There is a system, beginning from rest, with two masses, m1 and m2. M1 is on a table and attached to a rope that goes over a pulley (that is NOT massless)and attaches to hanging mass m1. Between m2 and the table there is a friction(kinetic) of 0.1
M1=10kg
M2=30kg
Mass of pulley=5kg and the Radius of the pulley is 0.3m.
Using conservation of energy, find, after m1 falls by 2m, the final velocity of m1 and the final velocity of m2. Also, find the angular acceleration of the pulley.
2. Relevant equations:
For kinetic energy:
K1=1/2 mv^2
K2=1/2 mv^2
And Kpulley= 1/2 Iw^2
For potential energy:
Ep=mgh
For work:
Wtotal=change in kinetic energy
W=m*d
W of gravity= negative change in potential energy

3. My attempt at this problem:
So since everything is attached together, I believe the final velocities 1 and 2 will be equal. By this reasoning, the final angular velocity of the pulley would be equal to the other velocities by the formula V= R(radius of pulley)*w
I used the Wtotal= deltaK and I plugged in all the forces relating to translational motion. However I wasn't sure if the tensions cancelled out. I assumed they did and therefore found The final velocity to be 2.65m/s. Then I used the formula Vf=R*wf and thus for the final angular momentum I to 8.83rads/second.
I think perhaps I should have somehow incorporated the rotational motion into it more, not just at the end. However, I was not quite sure how.

Thank you for taking time to help :D

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Last edited: Nov 28, 2014
2. Nov 28, 2014

### Orodruin

Staff Emeritus
How is the pulley going to accelerate if the tensions are the same?