Question

What is the magnitude of the resultant of a 100 newton force along the x-axis and a 150 newton force at an angle of 40° to each other?

Where do i start?? help!

Answer 1

Resolve each force into its x- and y-components, and add components algebraically. Finally, calculate the resultant of the two component sums.

Force angle x-comp y-comp
100N 0° 100N 0N
150N 40° 114.91 96.42

Resultant:
x-component=100+114.91=214.91N
y-component=0+96.42 = 96.42N
Magnitude of resultant
=sqrt(214.91²+96.42²)
=228.58N
Angle: atan(96.42/214.91)=atan(.44865)
=24.163°

Answer 2

What is a force angle? how did you get the 114.91?

Answer 3

x-component=150*cos(40°)=114.91N
y-component=150*sin(40°)=96.42N
The resultant is a single equivalent force pointing neither at 0° nor 40°, but somewhere in between.
It is calculated as the arcTan of the y component divided by the x-component, as above.