Solving Static Equilibrium: Force on Car from Rope & Tree

[Chuck 86]

Homework Statement

A student gets his car stuck in a snow drift. Not at a loss, having studied physics, he attaches one end of a stout rope to the vehicle and the other end to the trunk of a nearby tree, L = 12.2 m away, allowing for a small amount of slack, W = 0.400 m. The student then exerts a force F on the center of the rope in the direction perpendicular to the car-tree line,
If the rope is inextensible and if the magnitude of the applied force is 406 N, what is the force on the car? (Assume equilibrium conditions.)

Homework Equations

Sum of the forces?


Tryed sum of the forces i don't know really how to calculate the tensions(if that's what your supposed to do. any help will be appreciated

 

[tiny-tim]

Hi Chuck 86!

… Tryed sum of the forces i don't know really how to calculate the tensions(if that's what your supposed to do. any help will be appreciated

Well, that should have worked …

call both the tensions T (they'll be the same), and use geometry togehter with the fact that the sum of the forces on the centre of the rope will be zero.

(or draw a vector triangle )

What do you get? ​