SOLUTION: Find the resultant force R that will balance the three forces by adding a fourth mass to the force table at the appropriate angle. A. 300g @30° B. 450g @110° C. 400g @230°

Algebra ->  Test -> SOLUTION: Find the resultant force R that will balance the three forces by adding a fourth mass to the force table at the appropriate angle. A. 300g @30° B. 450g @110° C. 400g @230°      Log On


   

Question 1122981: Find the resultant force R that will balance the three forces by adding a fourth mass to the force table at the appropriate angle.
A. 300g @30°
B. 450g @110°
C. 400g @230°
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

   x-components:                     y-components

300∙cos(30°)  =  259.81          300∙sin(30°)  =  150.00
450∙cos(110°) = -153.91          450∙sin(110°) =  422.86
400∙cos(230°) = -257.12          400∙sin(230°) = -306.42 
--------------------------------------------------------
Total x-comp. = -151.22          Total y-comp. =  266.44

resultant magnitude = sqrt%28%28-151.22%29%5E2%2B%28266.44%29%5E2%29 = 306.36

tan(resultant angle) = 266.44%2F%28-151.22%29=-1.761936252

Since x-comp negative and y-comp positive,
resultant is in Quadrant II, so 
Resultant angle = 119.6°

So the force that will balance the three forces is a force
equal in magnitude to their resultant and in the opposite
direction, so we add 180° to the angle and the answer is

306.36g @ 299.6°

Note: The balancing force is NOT the resultant force, but
is in the opposite direction from the resultant force.  That's
why I added 180° to the angle.  You might mention this to your 
teacher.

Edwin