Physics final - quick help needed?

Sum of the forces must be equal to zero.

You'll have to break the forces into their x and y components first.

Force 1: 23.3 N, east (x component). Since it's directed towards east, there's no y component.

Force 2: 15,0 N, 60° north of east. To find the x and y components, we can use the trig functions.

x = cos 60° ∙ 15.0 N

x = 1/2 ∙ 15.0 N

x = 7.50 N, east.

y = sin 60° ∙ 15.0 N

y = √3/2 ∙ 15.0 N

y = 7.50√3 N, north.

So, the sum of the forces:

On the x axis, since both are on the same direction, we add them up: 23.3 + 7.50 = 30.8 N, east.

On the y axis, we only have on force: 7.50√3 N, north.

So, to cancel out everything, we have to apply a force that has an x component of 30.8 N (west) and y component of 7.50√3 N (south). To find the actual force, we use the pythagorean theorem:

x² + y² = r²

(30.8)² + (7.50√3)² = r²

948.64 + 168.75 = r²

r = √1117.39

r ≈ 33.4 N, there we have it, the magnitude.

Now, to find the angle, we can use any of these relations:

sin x = o/h, cos x = a/h, tan x = o/a

I'll just use cosine:

cos x = 30.8/33.4

cos x = 0.922

x = arccos 0.922

x ≈ 22.7° (SW), and that's an acceptable difference, since we rounded up the values a little bit.