Question

An object in equilibrium has three forces ex-
erted on it. A(n) 34 N force acts at 72.6, and
a(n) 47 N force acts at 25.9.
What is the direction of the third force?
(Consider all angles to be measured counter-
clockwise from the positive x-axis.)
Answer in units of degrees.

Answer 1

thats fine absoulelty fine

Answer 2

Sum the forces in the X and Y directions. Equilibrium occurs when the net force in each direction is zero. \[\text{Y:} \sum F_y = 0 = 34 \sin(72.6) + 47 \sin(25.9) + F_3 \sin(\theta)\]\[\text{X:} \sum F_x =0= 34 \cos(72.6) + 47 \cos(25.9) + F_3 \cos(\theta)\]

We can solve these two equations simultaneously for the two unknowns: \(F_3\) and \(\theta\)

Answer 3

A FBD is useful as well. This allows us to infer that the angle theta must be GREATER than 180, yet less than 270.