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Soumen Goswami (2446)

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Consider this problem
A rope of mass m and length L has 2 forces F1 and 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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