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I am wondering if the tension in the ropes in this situation is the same. Doesn't it matter if the other rope is pulled at an angle? Does this change the tension in the rope? For example if at one end there is a mass $m$, the tension in both of the ropes would be $mg $?

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    $\begingroup$ You need to tell us if there is any friction between the pulley and the rope on it. Then you need to tell us if the system is in static equilibrium, or if the mass hanging on the rope is accelerating due to the pull on the rope. $\endgroup$
    – Bob D
    Feb 2, 2019 at 21:32
  • $\begingroup$ No friction between the pulley and the rope .The mass is moving in uniform motion. $\endgroup$
    – Anon
    Feb 2, 2019 at 21:47
  • $\begingroup$ Good, then have you attempted to analyze the system with a free body diagram? $\endgroup$
    – Bob D
    Feb 2, 2019 at 21:55
  • $\begingroup$ Of course. But what confuses me is the angle . If you hold the pulley at that angle , shouldn't you pull harder (also horizontally to hold that pulley at that angle and also lifting the mass up ) ? $\endgroup$
    – Anon
    Feb 2, 2019 at 21:59
  • $\begingroup$ I should think so. It seems to me that as the angle increases the vertical component of the forces in both ropes supporting the mass decreases making it harder and harder to support the mass. $\endgroup$
    – Bob D
    Feb 2, 2019 at 22:26

2 Answers 2

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You are pulling at a constant velocity so no acceleration and no net force. Your are correct that $T=m\ g$. To pull the weight up over the pulley you have to pull with a force $m\ g$ no matter what the angle. If the left side of the rope is straight down, you have to pull on it with $m\ g$ to move with constant velocity. If there is no pulley and the rope is straight up, you have to pull with $m\ g$ to lift the weight. You pull with the same $m\ g$ at every angle between straight down and straight up.

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A massless, frictionless pulley only changes the direction of the rope. It does not change the magnitude of the force in the rope. Therefore, the tension T on one side of the pulley is the same as on the other side.

A way to verify that this must be true is to calculate the sum of the torques that the rope tension causes on the pulley. If the tensions were different values T1 and T2, then the sum of moments about the pivot point of the pulley = rT1-rT2 which does not equal 0. This would indicate that the pulley is accelerating (sum of Torque=I*alpha), but this violates the statement that the mass is not accelerating. Therefore, T1=T2 so that sum of the torque=0, and the rope tension=T on both sides of the pulley regardless of the angle.

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