# Calculate tension in a rope

MarliesM
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..

## Answers and Replies

Mentor
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.

grzz
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?

Mentor
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.

Staff Emeritus
Science Advisor
Homework Helper
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.

MarliesM
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).

Mentor
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.

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.

Gold Member
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?

Staff Emeritus
Science Advisor
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.

Mentor
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.

Gold Member
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.

Gold Member
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.