Calculate Rope Tension with Unequal Forces

[iampaul]

Homework Statement

How do i find the tension in a cord. If two equal forces,say F1 and F2, act on both ends of the cord the tension is F1=F2. What if the forces are not equal?
If a force A pulls one end of a rope, and a force B, pulls the other end and A is not equal to B, what is the tension in the rope.

Homework Equations

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The Attempt at a Solution

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[ehild]

If the rope has no mass, the forces at both ends are the same according to Newton's Third Law.
The forces can be different at the ends if the rope has mass and accelerates, or is subjected to gravity. In this case, the tension is different at different cross-sections inside the rope.

ehild

 

[iampaul]

thanks!

 

[fleem]

Technically, saying "the forces are equal" means they have equal magnitude and direction. Yes, the vast majority of readers will know what you mean but I've found its important to be somewhat pedantic in quiz questions. Otherwise a student can, for example, make the point I make here about the force, and its a valid point.

 

[rwisz]

To calculate the tension in a rope with unequal forces, you will need to use the formula T = F1 + F2, where T is the total tension in the rope, F1 is the force acting on one end of the rope, and F2 is the force acting on the other end of the rope. This formula works for any type of force, whether they are equal or unequal. In the case of unequal forces, the tension will be greater on the side with the larger force and smaller on the side with the smaller force. For example, if A is pulling with a force of 10 N and B is pulling with a force of 5 N, the tension in the rope will be 15 N towards the direction of A's force. It is important to note that the direction of the forces will also affect the direction of the tension in the rope.