Question

Four forces are acting on an object in static equilibrium: Force 1 has a magnitude of 46.0 N and is acting at an angle of 52 degrees above the positive x-axis. Force 2 has a magnitude of 29 N and is acting along the positive x-axis. Force 3 has a magnitude of 34.5 N and is acting along the negative y-axis. Find the magnitude of the last force, F4. Give your answer in newtons (N) and with 3 significant figures.

Answer 1

46N.[52o] + 29[0o] + 34.5[270o]+F4 = 0.
46*Cos52 + i46*sin52 + 29 -34.5i +F4=0
28.32 + 36.25i + 29 - 34.5i + F4 = 0.
57.32 + 1.75i + F4 = 0.
F4 = -57.32 - 1.75i.

X = -57.32 N., Y = -1.75 N.

F4 = sqrt(X^2 + Y^2).

Answer 2

57.34