Five forces act on an object. (1) 55 N at 90° (2) 40 N at 0° (3) 77 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?
___N at ___°
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Sum of forces is
55N j + 40N i - 77N j - 40N i + 25N i + 43.3N j
= 25N i - 21.3N j.
To obtain equilibrium you need -25N i + 21.3N j.
Magnitude is sqrt(25^2 + 21.3^2) = about 35N but use a calculator.
Direction is arctan(-21.3/25) = about 140 degrees but use a calculator.