How Much Force Does a Rope Exert on a Car in This Scenario?

[Windwaker2004]

Hi, can somebody help me out with this question:

A car is stuck on the side of the road and the driver has only a long piece of non-stretchable rope. Seeing a tree 20 m away from the car he ties the rope to the tree and then to the car such that it is quite tight and any sag is negligible. The driver then pushes the rope at the midpoint of the rope with a push prependicular yet horizontal to the line made by the rope. What force does the rope exert on the car if the driver can push the rope to a distance of 2 m with a force of 600 N?

I know (or atleast think) that I must use the similar triangles of the force and distance vectors. Any help would be greatly appreciated. Thanks!

 

[HallsofIvy]

Yes, similar triangles will do it (or right triangles which is the same thing). The rope is non-stretchable so if you press at the center point to move it a distance 2m, you form a right triangle with leg of length dx and hypotenuse of length 10m (half of the original 20m length). You can calculate the length of the other leg using the Pythagorean theorem. The distance the car moved is 20 m- that length- call it x.

The work done applying a force 600 N 2m is 1200 Joules. That would be the same as the work done to move the car distance x: Fx= 1200. Solve for x.

 

[Windwaker2004]

I don't need to solve for the distance the car moves. It's asking for the force (tension on rope) exerted on the car by the rope. I can't use the work equation either because this is for algebra and the teacher expects only algebraic equations not physics. Thanks anyway but I got help in the homework section with this.