Question

A rope of length L is pulled by a constant force f the tension in the Rope at the distance x from where the force f is applied

Answer 1

A rope of length L is pulled by a constant force f the tension in the Rope at the distance x from where the force f is applied

 From a distance x, one should take a small element dx

Mass of dx = Mdx/l=dm

The movement of rope proceeds along with acceleration a

The equation of motion regarding the small element dx is as follows:

{T + dT} - T = dm × a

dT = [M dx/l] × F/M

dT = F dx /l

Integration of both sides results as follows:

F(x. -F = - Fx/l

F(x. = F [1-x/l]

Answer 2

Mass of dx = Mdx/l=dm

The movement of rope proceeds along with acceleration a

The equation of motion regarding the small element dx is as follows:

{T + dT} - T = dm × a

dT = [M dx/l] × F/M

dT = F dx /l

Integration of both sides results as follows:

F(x. -F = - Fx/l

F(x. = F [1-x/l]