Tension is horizontal rope tied to hooks at each end

[Jwill]

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

Homework Statement

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.

Homework Equations

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...

 

[learningphysics]

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

 

[Jwill]

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

 

[Jwill]

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

 

[learningphysics]

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

yes.