Pulley System- equation derivation

AI Thread Summary
The discussion focuses on deriving the formula for the acceleration of a pulley system with a non-negligible cord mass. The initial attempt incorrectly applied the force equations, leading to confusion about the roles of tension and the forces acting on the masses. A suggestion was made to draw a free-body diagram to clarify the forces involved. The need for proper definitions of forces in the equations was emphasized to avoid misinterpretation. Overall, the conversation highlights the importance of accurately representing forces and tensions in mechanical systems.
hanlon
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Homework Statement



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

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

Homework Equations



F = ma

The Attempt at a Solution



Fby = Fax

Fby = mB *g

acceleration of system: a = (mB *g)/ma

acceleration of system with non-negligible cord

a = (mB + (mC * (lB/ l)))*g / (ma + (mC * (lA/ l)))need an answer check, I can't tell if its right.
 
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hanlon said:
3. The Attempt at a Solution [/b]

Fby = Fax

Fby = mB *g

acceleration of system: a = (mB *g)/ma

.

This is not right. Draw the free-body diagram, showing the forces both at A and B.
 
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
 
If you do not specify what Fbx and Fax are the equation Fbx=Fax has no sense.

ehild
 
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