Tension in a Uniform Cable: Where Does the Force Balance?

[Amar.alchemy]

Homework Statement

A uniform cable of weight w hangs vertically downward,supported by an upward force of magnitude w at its top end. What is the tension in the cable (a) at its top end; (b) at its bottom end; (c) at its middle? Your answer to each part must include a free-
body diagram. (Hint: For each question choose the body to analyze
to be a section of the cable or a point along the cable.) (d) Graph
the tension in the rope versus the distance from its top end.

Homework Equations

Newtons first law since the body is not accelerating.

The Attempt at a Solution

Actually i am not able to understand the problem itself. Particularly i am not able to understand the sentence "supported by an upward force of magnitude w at its top end" in the above problem statement. Kindly explain me??

 

[Dick]

I think it means what it says. Gravity exerts a downward force w on the cable and there is a balancing upward force w exerted at the top of the cable. So the cable is not accelerating since the net force on the cable is zero.

 

[ideasrule]

The phrase "supported by an upward force of magnitude w" is redundant. The rope is hanging and gravity exerts a downwards force w on it, so the pivot the rope hangs from must exert an upwards force w to prevent acceleration.

Hint for this problem: use the "black box" method. Once you choose a section of the rope to analyze, consider only the external forces acting on it; forget about the tension within the section.

 

[Amar.alchemy]

Thanks Dick and ideasrule :-)

So it means, the force exerted by the pivot is equal to its weight.