What is the tension in the rope of a pulley system in equilibrium?

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SUMMARY

The tension in the rope of a pulley system in equilibrium is determined by the forces acting on the system. In this case, a 50-kg mass experiences a downward gravitational force of 500 N, while a constant upward force of 200 N due to friction in the pulley results in a tension of 200 N in the rope. The equilibrium condition, where the sum of forces equals zero, clarifies that the tension is not equal to the weight of the mass when friction is present. Understanding the equilibrium condition is crucial for solving pulley problems accurately.

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  • Understanding of Newton's laws of motion
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  • Ability to apply free body diagrams
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  • Study the principles of Newton's second law in detail
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Homework Statement


When a 50-kg mass on a pulley is allowed to drop, the friction in the pulley creates a constant 200 N force upward. What is the tension in the rope?


Homework Equations


F (upward) = F (downward)


The Attempt at a Solution


I attempted this problem by assigning the upward force as 200 N and the downward force as mg, 500 N. My answer was 500 N but the correct answer is 200 N. Conceptually, this makes sense, but I cannot see how this works mathematically. Could someone please explain how equilibrium plays a role in pulley problems like this?
 
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If the mass is allowed to drop, then why would there be equillibrium? Maybe I'm misunderstanding the set-up?


Equillibrium is when \sum F=0 (and also \sum \tau =0)
 
Sorry, the applicable formula would be: F(upward) + ma = F (downward). I was confused with torque.
 

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