How to find tension in a rope when given the force?

[Amelina Yoo]

Q: In a tug of war between 2 athletes, each pulls on the rope with a force of 200N.

a) What is the tension in the rope?
b) If the rope does not move, what force is each athlete exerting on the ground?

I wrote for both a) and b) 200N, and I am unable to confirm this because my textbook has no answers. I am also not very confident with this question, and am unable to justify my answers. Can someone please explain how to do this question?

 

[haruspex]

Q: In a tug of war between 2 athletes, each pulls on the rope with a force of 200N.

a) What is the tension in the rope?
b) If the rope does not move, what force is each athlete exerting on the ground?

I wrote for both a) and b) 200N, and I am unable to confirm this because my textbook has no answers. I am also not very confident with this question, and am unable to justify my answers. Can someone please explain how to do this question?

Your answers are correct, except that in b) I assume the athletes also have some weight.
It sounds like a homework question. If so, it should have been posted in a homework forum.

 

[OldYat47]

Imagine the athlete on one end of the rope. If the rope had more than 200N tension then the athlete would be pulled toward the rope. So the tension in the rope is the same as the force exerted by each athlete, 200N. Suppose the feet of each athlete were affixed to the ground and that their weights are negligible. Let's look again at one athlete. That athlete is are pulling with a force of 200N, the tension in the rope is 200N, they are pushing toward the rope with their feet at 200N.

 

[haruspex]

Suppose the feet of each athlete were affixed to the ground and that their weights are negligible.

You would also need to assume that the athletes are almost flat to the ground.

 

[OldYat47]

Yes. If the weights are negligible then the forces all have to "line up" in a single line of action.