Answer to Question #283276 in Physics for riki

Question

Trying to get his car out of mud, a man ties one

end of a rope around the front bumper and the other end tightly

around a utility pole 18 m away. He then pushes sideways on the

rope at its midpoint with a force of 550 N, displacing the center of

the rope 0.30 m, but the car barely moves.What is the magnitude of

the force on the car from the rope? (The rope stretches somewhat.)

Answer 1

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

$$T=F/(2\sin\theta).$$

The angle is

$$\theta=\arctan\frac{0.3}{18/2}=1.9°.$$

The tension:

$$T=550/(2\sin1.9°)=8294\text{ N}.$$