Pulley System- equation derivation

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SUMMARY

The discussion focuses on deriving the formula for the acceleration of a pulley system with a non-negligible cord mass (mc). The key equation presented is a = (mB + (mC * (lB/ l))) * g / (ma + (mC * (lA/ l))). Participants emphasize the importance of including tension forces in the analysis and the necessity of clearly defining variables such as Fbx and Fax. The conversation highlights the need for accurate free-body diagrams to ensure correct force representation in the equations.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of free-body diagram construction
  • Familiarity with pulley systems and their dynamics
  • Basic principles of tension in strings and cords
NEXT STEPS
  • Study the derivation of acceleration in pulley systems with massless cords
  • Learn about the effects of cord mass on system dynamics
  • Explore advanced topics in mechanics, such as tension force calculations
  • Review examples of free-body diagrams in complex systems
USEFUL FOR

Students in physics, mechanical engineers, and anyone studying dynamics of pulley systems will benefit from this discussion.

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.
 
Last edited by a moderator:
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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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