Question

Two forces f1 and f2 are acting on a body one force is 4 times that of the other force and the resultant is equals to the greater force then the angle between the two forces

Answer 1

Answer:

Required angle s cos^(-1) ( - 1 / 8 ).

Explanation:

Let the forces are A( f1 ) and B( f2 ), where A > B.

 Here,

        A = 4B.   { greater is 4 times of lesser one }

Given, let the angle between them be C.

⇒ Resultant = A

⇒ A^2 + B^2 + 2ABcosC = A^2

⇒ A^2 + B^2 + 2( 4B )BcosC = A^2   { A = 4B }

⇒ A^2 + B^2 + 8B^2cosC = A^2

⇒ B^2 + 8B^2 cosC = 0

⇒ B^2( 1 + 8cosC ) = 0

⇒ 1 + 8cosC = 0

⇒ cosC = - 1 / 8

⇒ C = cos^(-1) ( - 1 / 8 )