Question

prove that, Tension is diffrent on both side in friction pulley.

Answer 1

Answer

Yes, Tension is diffrent on both side of pulley. if pully have friction/mass/strechable.

Proof:

This can be proved using the method of contradiction.

So, Let suppose, The tension is same on both side of string.

T' = T

τ = F × R × sin θ

τ  = TR sin 90° [tension(force) acting ⊥]

τ = TR [sin 90° = 1] .........(1)

This torque is acting "Clockwise" direction.

Also, τ' = TR sin θ

τ' = TR  ..........(2)

This torque is acting in "Anticlock" wise.

From 1 & 2,

τ = τ' (In magnitude)

But in both opposite direction.

So, They cancel each other And pulley will be in rest.

But As we know, pulley will must rotate so it contradict my supposition that tension is same on both side.

τ' ≠ τ' (including direction)

T ≠ T' (∵ R is constant there) [Proved]

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τ = torque

T = tension (Force)

R = radius of pulley

_______________

Amrit_____

Answer 2

Explanation:

Hi! Try to imagine the situation when you attach one body (mass m) to both ends of a string hung up by a pulley. Describe this system from the point of view of dynamics (Newton's II. Law). Important thing to note: you can also write Newton's Laws for different cross-sections of the string. This will probably lead you to the answer. I hope I could help a little :)