Why Does Tension Vary Along the Rope in a Hanging Superhero Scenario?

[ThePiGeek314]

Homework Statement

[/B]
Superhero and Trusty Sidekick hang motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation. (b) Find the tension in the rope above Superhero. (c) Find the tension in the rope between Superhero and Trusty Sidekick.

Homework Equations

F = ma
W = ga

The Attempt at a Solution

In the free-body diagram, I have Superhero being pulled down by gravity = 882 N, and Trusty Sidekick being pulled down by gravity = 539 N. The rope is pulling 882 N up on Superhero and 539 N up on Trusty Sidekick (definition of equilibrium, since they're motionless). I'm pretty sure the diagram is correct.

The total tension on the rope, since the mass of the rope itself is negligible = 882 + 539 = 1421 N. Because a rope pulls with equal tension on each object, the tension in the rope above Superhero is just 1421 N - the total weight it's being pulled down by.

Tension in the rope between Superhero and Trusty Sidekick should also be 1421, because tension is equal along the whole rope...but the answer is 539 N. How are the different forces at different points along the rope consistent with the tension remaining equal throughout the whole rope?

 

[BvU]

Hi Pi,
What if Sidekick let's go ? Would the tension in the lower part of the rope also be the same as in the top part ?

Can you post the free body diagram ?

 

[ThePiGeek314]

 

[haruspex]

View attachment 204867

That is not a free body diagram.

tension is equal along the whole rope

The fact that it is one continuous rope is confusing you. Think of it as two ropes with a join where Superhero is holding on.
Try to answer BvU's question. If Sidekick were not there, would the tension still be the same all along the rope?

 

[ThePiGeek314]

No, because the only weight on the rope would be Superhero's weight of 882 N. Using Newton's Third Law, the tension in the rope above Superhero would also be 882 N, right?

Using common sense, the tension in the rope below where Superhero is hanging on should be 0...but isn't tension supposed to be the same all along a rope?

 

[jbriggs444]

Nbut isn't tension supposed to be the same all along a rope?

Only if you refrain from pulling on the rope somewhere in the middle. If you've pulled on a real rope, you might notice that it is taut on one side of your hands and slack on the other.

In physics textbooks, one often uses massless, frictionless pulleys which exert zero longitudinal force along a rope. The ropes are also massless. The tension on a massless rope is indeed the same on either side of an ideal pulley. But we're not dealing with ideal pulleys here.