# Same Rope, DIFFERENT tensions?

by Legendon
Tags: rope, tensions
 P: 22 1. The problem statement, all variables and given/known data 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? 2. Relevant equations 3. 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. Attached Thumbnails
HW Helper
PF Gold
P: 6,040
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.
 P: 22 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 ??? Attached Thumbnails