Yvette hangs a 2.4 kg bird feeder in the middle of a rope tied between two trees. The feeder creates a tension of 480 N in each side of the rope. If the two trees are 4.0 m apart, how much will the rope sag in the center?

Question

Yvette hangs a 2.4  kg bird feeder in the middle of a rope tied between two trees. The feeder creates a tension of 480 N in each side of the rope. If the two trees are 4.0 m apart, how much will the rope sag in the center?

shane_b · Answer

First you should draw it out so that you can picture the forces:
|dw:1360207844953:dw|
From that should notice that each side must be pulling up with a force of:$$F=(480N )sin(\theta)$$Twice that force must equal the weight of the bird feeder (mg) so:$$(2)(480N)sin(\theta)=mg=(2.4kg)(9.8m/s^2)=23.54N$$
Next you need to find the angle:$$arcsin(\frac{23.54}{960})=1.4 \space  degrees$$
You can finally find the sag height using:$$tan(1.4)=\frac{opp}{2m}$$$$(2m)tan(1.4)=0.049m$$