Why Are Tensions Different in the Same Rope?

[Legendon]

Same Rope, DIFFERENT tensions?

Homework Statement

Consider the system shown with m1 = 20.0 kg, m2 = 12.5 kg, R = 0.200 m, and the mass of pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.00 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley. (a) Calculate the time interval required for m1 to hit the floor. (b) How would your answer change if the pulley were massless?

Homework Equations

The Attempt at a Solution

The solution is fine but i cannot comprehend in the first place why the tensions are not equal. I thought in the same string the tension is the same? And in part b, i think the tension is the same for both T1 and T2.

 

[PhanthomJay]

I don't understand what you mean when you say

The solution is fine but i cannot comprehend in the first place why the tensions are not equal.

Since you're OK with the solution, you must realize that the tensions must be unequal in order to get an unbalanced torque on the pulley so that it angularly/tangentially accelerates consistent with the linear acceleration of the blocks. The tensions are equal, as you noted, only if the pulley is massless and frictionless (an ideal pulley) or if it is of negligible mass and friction such that the results are close enough by making the assumption of an ideal pulley.

 

[Legendon]

Thanks, i can understand that part. That it is the difference in torque that causes the acceleration when pulley has mass now this one is giving problems.
The motor right powers the system causing the rigid object left to spin clockwise. So when my prof drew the FBD of the rigid object, the tensions are both pointing away to the right. I expected the tension on top to point to the right and bottom to point left. Why are both pointing right ?

 

[PhanthomJay]

Thanks, i can understand that part. That it is the difference in torque that causes the acceleration when pulley has mass now this one is giving problems.
The motor right powers the system causing the rigid object left to spin clockwise. So when my prof drew the FBD of the rigid object, the tensions are both pointing away to the right. I expected the tension on top to point to the right and bottom to point left. Why are both pointing right ?

This same question could be asked for the original problem. Tension forces ALWAYS pull away from the object on which they act. If you hoist up a pail of water using a pulley attached to the ceiling (an Atwood machine), the side of the rope with the pail moves up, and the side that you are pulling on moves down, but on both sides, the rope tension force on the pulley acts down, right? And by Newton 3, the rope tension force on the pail and the rope tension force on your pulling hand acts up, right?