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

AI Thread Summary
In a pulley system with a 50-kg mass, the upward force due to friction is 200 N, while the downward force from gravity is 490 N (not 500 N). The tension in the rope is equal to the upward force when the system is in equilibrium, which is 200 N. The confusion arises from misunderstanding the concept of equilibrium; even if the mass is allowed to drop, the forces must balance for the system to be in a state of equilibrium. The correct application of the force equation shows that the net force must equal zero when in equilibrium. Understanding these principles clarifies the tension in the rope during such scenarios.
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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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