Question

two forces p and q making an angle of 60 with each other act at a point. P has a magnitude of 8 Newton and the resultant of two forces has magnitude of root 84 Newton. Find the magnitude of q and direction of resultant.
If don't know how to solve it then skip the question and please don't post irrelevant answers. ​

Answer 1

Answer:

Explanation:

Let Ф be angle between Forces P and Q

Acc. to parallelogram law,

R² = P² + Q² + 2PQ cosФ

84 = 64 + Q² + 2(8) Q cos60⁰

20 = Q² + 16Q (1/2)                                          ∵cos 60° = 1/2

Q² + 8Q -20 = 0

Q² + 10Q -2Q - 20 = 0  

Q(Q + 10) - 2(Q + 10) = 0

(Q - 2) (Q + 10) = 0

So, Q = 2  Newton                      (Rejecting Q=-10 since magnitude cant be -ve)

Let resultant make angle α with Force P

tan α = QsinФ/ P + QcosФ

tan α = 2 sin60°/ 8 + 2 cos 60°

        = 2 (√3/2) / 8 + 2(1/2)

        =√3/9

tan α =1/ 3√3

   

Answer 2

Answer:

sorry if I made any mistakes

Explanation:

solution is attached

|q| = 2N

direction of resultant - tan alpha = √3/9