# Systems in equilibrium

1. Aug 5, 2014

### brake4country

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
F (upward) = F (downward)

3. 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?

2. Aug 5, 2014

### Nathanael

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 $\sum \tau =0$)

3. Aug 5, 2014

### brake4country

Sorry, the applicable formula would be: F(upward) + ma = F (downward). I was confused with torque.