Finding Equilibrium: Solving a Force Problem

[Macleef]

Homework Statement

A box with a weight of 215 N rests on a ramp. There is a frictional force of 27 N exerted on the box directed up the ramp. If the ramp is inclined at 30 degrees, what force must be applied at an angle of 40 degrees to the ramp to maintain equilibrium?

Textbook Answer: 80.5 N and 105 N

Homework Equations

u (dot) v = |u||v|cosx

The Attempt at a Solution

F = 215(cos30) = 186.2 N
F = 27(cos20) = 25.37 N
F = 215(cos40) = 164.7 N
F = 242(cos40) = 185.38 N
F = 242(cos70) = 82.77 N

None of them are right and I don't know how else to solve this problem.

 

[HallsofIvy]

What reason do you have to think that the answer will be given by a single dot product? Draw a picture of the situation and think about it.