Physics - Tension question

[JoyantBuoyant]

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Okay, if one person pulls a rope 2000N to the left and another person pulls the rope 2000N to the right, what is the Tension in the rope ?

The answer is 2000N but I really dont understand the reasoning, I thought it was 4000N. Can someone please possibly explain how to approach tension problems and the basics I should know for tension ?

 

[chem4ever]

Okay, if one person pulls a rope 2000N to the left and another person pulls the rope 2000N to the right, what is the Tension in the rope ?

The answer is 2000N but I really dont understand the reasoning, I thought it was 4000N. Can someone please possibly explain how to approach tension problems and the basics I should know for tension ?

Think of it this way. Since both people are applying the same amount of force in opposite directions, then the rope is in static equilibrium and will not move. Now let's look at the forces on one side of the rope (where one of the people are holding it). That person is applying 2000 N in his direction which means that in order for the rope not to move, the rope must have a 2000 N force in the opposite direction. That force is the tension in the rope. And since the rope is in a straight line with no friction acting on it at any point, then the tension in the rope must be the same everywhere. Thus, the tension in the rope anywhere must be 2000 N.

For these kind of questions, it's helpful to find a place on the rope that is easy to figure out and then apply it to the rest of the rope.

Hope this helps.

 

[SKaminski]

Imagine that the rope was instead tied to a tree. As you pull away with 2000N worth of force, does the tree move? No? Why not? Newtons Third Law. The tree is already inherently resisting with that force, and now it's being explicitly stated.

 

[regeneration]

And what if we have one side being pulled on at 3000N and the other at 2000N (For example a helicopter being accelerated up at 3000N holding a block weighing 2000N)? I believe the tension would now be 3000N

 

[milski]

If the rope is tense and is staying tense, there is no such case. If the rope is non-elastic, the tension and the forces pulling on its both sides will be the same. In your helicopter case (what does it mean to be accelerated at 3000 N anyway?) the tension on the side of the block will be more than the weight of the block.

The simplest way to look at it is from Newton's 3rd law: the force on one side of the rope has the same magnitude as the tension. Tension cannot change over the length of the rope (or the rope is expanding or collapsing) and the force at the other end will have the same magnitude as the tension and the initial force.

 

[regeneration]

If the rope is tense and is staying tense, there is no such case. If the rope is non-elastic, the tension and the forces pulling on its both sides will be the same. In your helicopter case (what does it mean to be accelerated at 3000 N anyway?) the tension on the side of the block will be more than the weight of the block.

The simplest way to look at it is from Newton's 3rd law: the force on one side of the rope has the same magnitude as the tension. Tension cannot change over the length of the rope (or the rope is expanding or collapsing) and the force at the other end will have the same magnitude as the tension and the initial force.

This only applies to a non-accelerating system. My claim is for an accelerating system with a mass attached to the accelerating system by a taut rope. In this situation, the tension will be the mass of the system * acceleration of the system (What I implied by 3000N acceleration)

 

[milski]

This only applies to a non-accelerating system. My claim is for an accelerating system with a mass attached to the accelerating system by a taut rope. In this situation, the tension will be the mass of the system * acceleration of the system (What I implied by 3000N acceleration)

Yes, and in that case the forces pulling on both sides of the rope will be 3000N as well. There is no way to have the tension change over the length of the rope without breaking up the rope.

If you want, you can treat the rope as a chain of infinitesimal pieces of rope and apply the 3rd law for each adjacent pair of pieces.

 

[JoyantBuoyant]

got it thanks, the latter part of this discussion confused me a bit so I'm just going to ignore i read that part lol. Thanks guys !