Question

In order to get his car out of the mud, a man ties one end of a rope to the front bumper and

the other end to a tree 15 m away, as shown below. He then pulls on the center of the rope

with a force of 400 N, which causes its center to be displaced 0.30 m, as shown. What is the

force of the rope on the car?

Answer 1

Answer

The magnitude of the force on the car from the rope is

$T=\frac{F}{2sin\theta}\\\theta=tan^{-1}(\frac{F}{2T}) \\\theta=tan^{-1}(\frac{0.30}{7.5})\\\theta=2.29°$

Now

So tension is

$T=\frac{400}{2sin2.29°}\\=5005.33N$