Auniform rope of length l is pulled by a constant force f. what is the tension in the rope at a distance l from the end, where it is applied?

Imagine the rope tied to a hook on the ceiling. And then attach a weight to the rope. You have your situation exactly as described. The tension is equal all along the rope and will be the amount of the weight of the rope plus the weight of your load. You may ignore the weight of the rope if it is small compared to the load. If you are considering a horizontal suspension then the result is still the same at any point on the rope. The rope conforms to a curve known as a Catenary. Which is a class of curves that are all hyperbolic. If you have the formula for the curve you can figure out the forces. and they will all be uniform along the suspending cable. Look up Catenary

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