Answer "Homework: P & Q Forces Resultant & Angle

[kalupahana]

Homework Statement

The resultant of two forces P & Q is √3Q. It make angle of 30^o with the direction of force P. Show that P is either equal to Q or equal to 2Q.

Homework Equations

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

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.

 

[anathema]

To find the values of P, you can use the trigonometric identity cos^2Θ + sin^2Θ = 1 and substitute for sinΘ in equation (2). This will give you an equation with P as the only unknown variable, which you can then solve for to find the possible values of P.