# 2 masses suspended over a pulley, finding a mistake

1. Jun 6, 2014

### aquance

1. The problem statement, all variables and given/known data
http://i.imgur.com/1j19V0n.jpg
Two masses are suspended from a pulley as on the pic. I have pulleys radius R and moment of inertia I and masses m1 m2.

2. Relevant equations

3. The attempt at a solution

So 2nd law of motion:

$$N_{1} - m_{1}g=m_{1}a$$
$$m_{2}g-N_{2} = m_{2}a$$
$$(N_{2}-N_{1})R=Iε=\frac{Ia}{R}$$

I get N's from 3rd equation and add two first ones

$$N_{2}-N_{1}=\frac{Ia}{R^{2}}$$
$$g(m_{2}-m_{1}) + N_{1} - N_{2} = (m_{1}+m_{2})a$$

sub N's to second equation

$$g(m_{2}-m_{1}) - \frac{Ia}{R^{2}} = (m_{1}+m_{2})a$$
$$g(m_{2}-m_{1}) = (m_{1}+m_{2})a + \frac{Ia}{R^{2}}$$
$$g(m_{2}-m_{1}) = a(m_{1}+m_{2}+\frac{I}{R^{2}})$$
$$\frac{g(m_{2}-m_{1})}{m_{1}+m_{2}+\frac{I}{R^{2}}} = a$$

Now, it's wrong as there should be 2I and not I. Where did I make a mistake?

2. Jun 6, 2014

ehild

3. Jun 6, 2014

### aquance

Uh, thanks, it seems that prof made a mistake.

4. Jun 6, 2014

### ehild

Everybody can make mistakes....

ehild