Understanding Tension Force: Two Elephants Pulling a Rope

[oxnume]

Homework Statement

Two elephants are pulling on opposite ends of a rope each with 10N of force. What is the tension force experienced by the rope?

Homework Equations

Not sure if there are any

The Attempt at a Solution

I originally thought to just add the the two together because they are pulling in opposite directions, so that would be 20N. But after taking up this question in class my teacher said the answer is supposed to be 10N and didn't explain too clearly. Can someone please explain exactly why that is?

 

[tiny-tim]

Welcome to PF!

Hi oxnume ! Welcome to PF!

Two elephants are pulling on opposite ends of a rope each with 10N of force. What is the tension force experienced by the rope?
…
my teacher said the answer is supposed to be 10N and didn't explain too clearly. Can someone please explain exactly why that is?

Because that's the way tension is defined …

if a mass of 10N is hanging from a rope tied to the ceiling, then the force exerted by the rope on the mass is (obviously) 10N …

so, by Newton's third law, the mass is also exerting 10N on the rope …

and since the rope isn't moving, Newton's second law tells us that the forces on the two ends of the rope must add to zero …

so the ceiling is also exerting 10N on the rope

(and the rope is exerting 10N on the ceiling).

Tension of 10N means that every tiny little bit of the rope has 10N force on either side of it, holding it in place.