Physics Equilibrium

Question

A 4.30 kg sign hangs from 2 wires. The left wire exerts a 31.0 N force at 122 degrees. What is the magnitude of the force exerted by the 2nd wire?

Answer 1

The left wire has x and y components of X = 31.0 N x cos 122 = -16.4 N and Y = 31.0 N x sin 122 = 26.3 N. The right wire must have an x component equal and opposite to the x component of the left wire. The right wire must have a Y component equal to the difference between the weight of the picture 4.3 kg x 9.8 m/s^2 = 42.1 N and the Y component of the left wire or

Y_right = 42.1 N - 26.3 N = 15.8 N.

The magnitude of the force on the right wire is gotten by √ 16.4^2 + 15.8^2 = 22.8 N using the pythagorean theorem on the X and Y components of the right wire.