# FInd force P

#### kalupahana

1. The problem statement, all variables and given/known data
The resultant of two forces P & Q is √3Q. It make angle of 30o with the direction of force P. Show that P is either equal to Q or equal to 2Q.

2. Relevant equations
R2 = P2 + Q2 + 2PQcosΘ
tanα = QsinΘ/[P+QcosΘ]

3. The attempt at a solution
From R2 = P2 + Q2 + 2PQcosΘ

3Q2 = P2 + Q2 + 2PQcosΘ
2Q2 = P2 + 2PQcosΘ
4Q2 = P[P+QcosΘ]---------------(1)

From tanα = QsinΘ/[P+QcosΘ]
tan 30 = QsinΘ/[P+QcosΘ]
1/√3 = QsinΘ/[P+QcosΘ]
P+QcosΘ = √3QsinΘ-------------------(2)

replacing 1 with 2
4Q2 =√3 PQsinΘ
PsinΘ = 4/√3

from here what should I do to find the values of P.

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