If two people pull on either side of the rope with a force of 65N, why is the tension in the rope 65N?

1 Answer
Jan 19, 2017

Apply Newton's third law. See below.

Explanation:

The rope experiences the same pulling force on both sides, and therefore it is in a state of static equilibrium (i.e. it is at rest consequently has a net force of zero).

A force diagram:

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Where vecF_1 and vecF_2 are the pulling forces on the rope and vecT is the tension force. R will represent the rope later.

Here we consider Newton's third law.

Newton's third law states that every force occurs as a member of an action/reaction pair of forces. You may know it as the familiar phrase, "every action has an equal and opposite reaction." Most importantly, two members of an action/reaction pair are equal in magnitude but opposite in direction.

vecF_(A on B)=-vecF_(B on A)

In this situation, each person pulls on the rope with 65N of force, so:

vecF_(1 on R)=65N and vecF_(2 on R)=65N.

This tells us that the pulling force exerted by each person on the rope is 65N, and consequently by NIII, the rope exerts an equal but opposite tension force of 65N on each person.

This is an action reaction pair. Therefore:

vecF_(R on 2)=vecF_(2 on R)=vecF_(1 on R)=vecF_(R on 1)=65N

The tension force in the rope, given by vecF_(R on 1) and vecF_(R on 2), is therefore 65N.