Posted by **Lexie** on Saturday, December 15, 2012 at 4:58pm.

Five forces act on an object.

(1) 63 N at 90°

(2) 40 N at 0°

(3) 83 N at 270°

(4) 40 N at 180°

(5) 50 N at 60°

What are the magnitude and direction of a sixth force that would produce equilibrium?

- Physics -
**Damon**, Saturday, December 15, 2012 at 5:21pm
find sum in x direction

63 cos 90 + 40 cos 0 + 83 cos 270 + 40 cos 180 + 50 cos 60

=50 cos 60 = 25 N at 0 deg

find sum in y direction

63 sin 90 + 40 sin 0 etc = 23.3

tan theta = 23.3/25 = .932

theta = 43

we want equal and opposite

so 43 + 180 = 223 degrees

magnitude = sqrt (625+543)

= 34.2 Newtons

- Physics -
**Mike**, Thursday, February 5, 2015 at 10:52am
For others to be able to solve:

I'm using variables since I'm use to computer science

N = newtons // number after is force number, x is angle

T1 = N1 cos A, N2 cos A, N3 cos A, etc

T2 = N1 sin A, N2 sin A, N3 sin A, etc

D = TAN-1(T1/T2) //use calculator

direction = D + 180

magnitude = sqrt(T1ˆ2 + T2ˆ2)

I liked your answer Damon.

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