How can I calculate the tension in a rope?

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    Rope Tension
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Discussion Overview

The discussion revolves around calculating the tension in a rope when subjected to different forces by two individuals pulling in opposite directions. Participants explore concepts related to equilibrium, the effects of mass on tension, and the implications of different force magnitudes on the behavior of the rope.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about calculating tension when two people pull on a rope with different forces, noting that tension is the same throughout a rope in equilibrium.
  • Another participant asserts that for massless ropes, both sides must be pulled with the same force, implying that differing forces cannot exist simultaneously.
  • Some participants discuss the scenario where one person pulls with force F and the other with 2F, questioning whether the system would accelerate and how tension would vary if the rope had mass.
  • There is a suggestion that if the rope has mass, the tension would differ along its length, with one end experiencing a force of F and the other 2F.
  • One participant mentions that a real rope would sag and require a vertical component of force to counteract gravity, while another questions how the rope remains stationary if only horizontal forces are applied.
  • Discussion includes humorous speculation about the implications of maintaining a force difference indefinitely and the physical limitations of the individuals involved.
  • Clarifications are made regarding the differences between massless and massive ropes, with emphasis on how forces are transmitted along the rope and the time it takes for changes in force to propagate.

Areas of Agreement / Disagreement

Participants express differing views on the nature of tension in ropes, particularly regarding massless versus massive ropes. There is no consensus on how to calculate tension in the given scenario, and the discussion remains unresolved.

Contextual Notes

Participants highlight assumptions regarding the mass of the rope and the conditions under which tension is calculated. The discussion includes unresolved questions about the behavior of the rope under different force conditions and the implications of mass on tension.

MarliesM
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Hi,

I'm a bit confused with determining the tension in a rope. For example, when two people are puling on a rope, one with a force F and the other with a force 2F, how can you calculate the tension? I know the tension at any point in a rope is the magnitude of force acting at that point, and that the tension is the same everywhere if the rope is in equilibrum. But I can't figure out what to do next..

I hope someone can help me, since I'm kind of stuck on every physics problem involving tension..
 
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MarliesM said:
For example, when two people are puling on a rope, one with a force F and the other with a force 2F, how can you calculate the tension?
For massless ropes that cannot happen. Both sides must be pulled with the same force.
 
If one person is pulling with a force F and the other is pulling on the same rope with 2F in the opposite direction then would not the whole thing would accelerate by a resultant force of F in the direction of 2F?
 
grzz said:
If one person is pulling with a force F and the other is pulling on the same rope with 2F in the opposite direction then would not the whole thing would accelerate by a resultant force of F in the direction of 2F?
If the rope had mass, yes. And then the tension in the rope would vary from a value of F at one end to a value of 2F at the other.

But I doubt that that's what the OP has in mind.
 
Fnet = ma​

If an object has either (1) negligible mass, or (2) constant or zero velocity (a=0), then the net force must be zero.
 
Thank you for all your replies, I see my F-2F theory didn't make sence.

I still have trouble with tension though.. For example; if two people are pulling on a rope (with a force F) then how come the rope doesn't fall, since there are no upward forces to counter gravity?

(excuse me for my bad English, it's not exactly my native language).
 
MarliesM said:
I still have trouble with tension though.. For example; if two people are pulling on a rope (with a force F) then how come the rope doesn't fall, since there are no upward forces to counter gravity?
Because it's massless and thus weightless. :wink:

A real rope has mass and weight and would sag a bit between the two people. They would end up exerting a vertical component of force to support the weight of the rope.
 
Doc Al said:
If the rope had mass, yes. And then the tension in the rope would vary from a value of F at one end to a value of 2F at the other.

So the rope then would continuosly stretch until the end of time so that the difference of 2F and 1 F would always hold?
 
256bits said:
So the rope then would continuosly stretch until the end of time so that the difference of 2F and 1 F would always hold?
The stronger guy (the 2F one) would find himself having to run faster and faster to maintain that steady 2F tension in the rope. Eventually, he'd probably trip over something, or his shoes would melt or he'd fall over the edge of the earth.
 
  • #10
256bits said:
So the rope then would continuosly stretch until the end of time so that the difference of 2F and 1 F would always hold?
I don't understand what you mean by 'continuously stretch until the end of time'. Subject to a net force, the massive rope will continue to accelerate--just like any other object.

How long the two people could maintain such a force difference on a piece of rope is another story. Not for long.
 
  • #12
NascentOxygen said:
The stronger guy (the 2F one) would find himself having to run faster and faster to maintain that steady 2F tension in the rope. Eventually, he'd probably trip over something, or his shoes would melt or he'd fall over the edge of the earth.

Superman and The Flash tug of war. Cool.
 
  • #13
Doc Al said:
I don't understand what you mean by 'continuously stretch until the end of time'. Subject to a net force, the massive rope will continue to accelerate--just like any other object.

How long the two people could maintain such a force difference on a piece of rope is another story. Not for long.

Sorry DocAl
Massless rope and a rope with mass. My cryptic message was to get someone to respond with the difference, but no luck.

A massless rope is idealized so that it offers no resistance to force. A force on one end would be transmitted immediately to the other end. The tension in the rope is a constant anywhere along its length.

For a real rope, with a mass, a force on one end will take some time to be felt at the other end. A change in force is not transmitted instantaneously to the other end, but travels down the rope much like a sound wave in air.

That would be a fair simple description.
 

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