Why Does a Pulley System Show Different Tensions for Different Masses?

[Psi]

I am working out a homework problem in which two unequal masses are on either end of a rope, which is wrapped around a pulley. The problem asks what the tension is in the part of the rope holding "(a) the lighter block, and (b) the heavier block". The solution manual reports different answers for these parts, but I thought tension was always the same in the same rope...?

Am I right? If not, could you explain what is happening in this problem?

Thanks a lot!

--Psi

 

[Doc Al]

Originally posted by Psi
The solution manual reports different answers for these parts, but I thought tension was always the same in the same rope...?

Tension would be the same if the rope were massless and the pulley were massless and frictionless. Consider that the rope exerts torque on the pulley.

 

[M98Ranger]

Hello Psi,

Thank you for reaching out about this tension problem. It is understandable that you are confused about the different answers reported in the solution manual. While it is true that tension is always the same in the same rope, it is important to consider the different forces acting on the rope in this particular scenario.

In this problem, the two unequal masses are exerting different forces on the rope due to gravity. The heavier block exerts a greater downward force on the rope, while the lighter block exerts a smaller downward force. This means that the tension in the rope will be different in each section, as the tension is equal to the force applied on the rope.

To better understand this, let's think about the forces acting on the rope. On one side, we have the tension force pulling the rope upwards, and on the other side, we have the weight of the heavier block pulling the rope downwards. In order for the rope to remain in equilibrium, the tension force must be equal to the weight of the block. This means that the tension in the section of the rope holding the heavier block will be greater than the tension in the section holding the lighter block.

I hope this explanation helps clarify the concept of tension in this problem. It is important to always consider the different forces acting on an object when determining the tension in a rope. Please let me know if you have any further questions or concerns.