Force applied on cable attached to car and tree

[Ab17]

Homework Statement

your car is stuck in the mud and you can’t pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle u from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for thecasewhereu57.00°andf 5100N

Homework Equations

Efx=0
Efy=O

The Attempt at a Solution

Efx
T1cos@ = t2cos@
T1=T2
Efy=0
F = 2tsin@

Is this right?

 

[CWatters]

F = 2tsin@

Close. That's an equation for F.

The angle is defined in the problem as "u" rather than "@".

 

[Ab17]

But is the method of solution correct besides the u?

 

[CWatters]

Your answer is correct if you rearrange it to give an equation for T.

I don't understand your method.

 

[CWatters]

I would solve it by drawing a fbd for the point on the rope where f Is applied.