IIT JEE , AIEEE Forum - Physics , Mechanics

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Consider this problem
A rope of mass m and length L has 2 forces F₁and F₂ applied at its end points.. find the expression for tension at any point in the rope.
Here is the solution to this problem
consider a length x of the rope from the end where F₂ is acting. Let the tension at the other end be T.
Mass of this portion of the rope = (m/L)x
Acceleration of the rope = (F₁ - F₂)/m
So
T - F₂ =[ (m/L)x] [(F₁ - F₂)/m]
T = F₂ +[(F₁ - F₂)/L]x
At x = L/2
T = (F₁ + F₂)/2
Hence the tension at the midpoint is
T = (100 + 70)/2 = 85 N

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