# Classical Mechanics - Pulleys System

1. Jun 20, 2009

### TomAlso

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

Consider the pulleys system in the picture. Assume both pulleys are frictionless. Assume the rope is massless and inextensible. Find the acceleration of the mass $$m_2$$

2. Relevant equations

3. The attempt at a solution

I have solved the same problem with massless pulleys and I fail to see if their radii should be involved at all in the final result. So first notice that the acceleration of the mass $$m_2$$ is half of the acceleration of the mass $$m_1$$. On $$m_1$$ we have:

$$m_1 g - T = m_1 a$$

On $$m_2$$ we have:

$$2T - (m+m_2)g = (m+m_2) \cdot \frac{a}{2}$$

which solves for

$$a = \frac{2*(m + m_2 - 2 m_1)}{4 m_1 + m + m_2}$$

Anyone can offer any advice? In particular, how am I supposed to include the radius of the pulleys and the pulley that does not figure in the equation? Thank you!

#### Attached Files:

• ###### pulleys.jpg
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2. Jun 21, 2009

can you post the picture a different way? I can't see the attachment

3. Jun 21, 2009

### TomAlso

The picture is just like http://img84.imageshack.us/i/carrucoleesameot5.jpg/" [Broken]. Both pulleys have mass $$m$$ and radius $$r$$. The mass labeled A is $$m_1$$ and B is $$m_2$$.

It says my attachment is pending approval, maybe that is the problem.

Last edited by a moderator: May 4, 2017
4. Jun 21, 2009

### Staff: Mentor

(1) Since the pulleys have mass, you cannot assume that the tension in the rope is the same throughout. Treat each rope segment as having a different tension; Label the tensions T1, T2, and T3.
(2) Don't ignore the rotational inertia of the pulleys. I presume that you can model the pulleys as uniform disks. (You'll need to analyze both pulleys.)