Pulley System- equation derivation

[hanlon]

Homework Statement

Determine a formula for acceleration of the system shown in Fig. 4-45 if the cord has a non-negligible mass m_c. Specify in terms of l_A and l_B, the length of cord from the respective masses to the pulley ( The total cord length is l= l_A + l_B)

[PLAIN]http://img706.imageshack.us/img706/8575/3333v.png

Homework Equations

F = ma

The Attempt at a Solution

F_by = F_ax

F_by = m_B *g

acceleration of system: a = (m_B *g)/m_a

acceleration of system with non-negligible cord

a = (m_B + (m_C * (l_B/ l)))*g / (m_a + (m_C * (l_A/ l)))need an answer check, I can't tell if its right.

 

[ehild]

3. The Attempt at a Solution [/b]

F_by = F_ax

F_by = m_B *g

acceleration of system: a = (m_B *g)/m_a

.

This is not right. Draw the free-body diagram, showing the forces both at A and B.

 

[hanlon]

Is my whole solution wrong, or just the forces I used.

I understand now that I didn't use tension force, but is the way I derived the equation wrong with

Fby = Fax

 

[ehild]

If you do not specify what Fbx and Fax are the equation Fbx=Fax has no sense.

ehild