Acceleration of masses in a pulley system

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SUMMARY

The discussion focuses on the calculation of acceleration in a pulley system involving two masses: a 2kg block and a 7kg block. The user derived the tension (T) as 29.36N but questioned the accuracy of their equation due to discrepancies in the results. Key corrections identified include the need for proper denominators in the equations and the correct sign for the friction term, which should be negative. The user mistakenly applied static friction principles instead of dynamic ones, leading to incorrect assumptions about the masses.

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  • Understanding of Newton's laws of motion
  • Familiarity with pulley systems and tension calculations
  • Knowledge of friction types, specifically static vs. dynamic friction
  • Basic trigonometry for resolving forces at angles
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jisbon
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Homework Statement
2 masses on each side of the inclined plane. Coefficient of kinetic friction = 0.3, held by an inextensible string.
Masses of blocks as labelled on the diagram
Relevant Equations
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1573733245458.png


So I figured out the equation, but it is probably wrong because the answer doesn't tally.
Since the string is inextensible, I can assume that tension is the same for both sides, and acceleration for both masses is the same too So:
I can say that the acceleration of 2kg block =acceleration of 7kg block

$$\dfrac {7g\sin 40-T}{2+7}=\dfrac {T+\left( 0.3\right) \left( 2g\cos 50\right) -2g\sin 50}{7+2} $$

I got T = 29.36N, and used one of the equation to get my acceleration. However, it seems to be wrong :/

Is there something wrong with my equation? Thanks
 
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The denominator of the first terms should be 7 and the denominator of the 2nd term should be 2, and the sign of the friction term should be negative.
 
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Chestermiller said:
The denominator of the first terms should be 7 and the denominator of the 2nd term should be 2, and the sign of the friction term should be negative.
Mistaken it for static friction and the massess too. Thanks for the help
 

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