# Tension is horizontal rope tied to hooks at each end

1. Sep 21, 2007

### Jwill

Want to make sure I'm doing this right... it seems too easy

1. The problem statement, all variables and given/known data
A horizontal rope is tightly tied to hooks between two walls separated by a distance of 5m. A 100N weight is suspended from the middle of the rope and it sags so that the middle of the rope is displaced a distance of 0.25m.

a. What is the tension in the rope?
b. What are the horizontal and vertical forces exerted on the hooks.

2. Relevant equations

3. The attempt at a solution
I found the angle using arcTan(.25/2.5) = 5.7106 degrees. Then did 100N/tan(5.7106)=1000Ni and used sqrt(100N^2 + 1000N^2)= 1004.988N to find the rope's tension...

2. Sep 21, 2007

### learningphysics

The tension is half that... the vertical component of tension on either side of the weight has to be 50N.

3. Sep 21, 2007

### Jwill

okay, thanks, i was thinking that might be the case

4. Sep 21, 2007

### Jwill

So that would also make the horizontal forces on each hook 500N right?

5. Sep 21, 2007

yes.