Two forces F1=20N and F2=30N are acting on an object so, 1) find the net force acting on an object. 2) state the direction of the net force acting on the object? 3) if the body does not none under the application of these forces and what can be the possible reason for this. Identify the and its direction.

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Solution

$L e t f 1 a n d f 2 a r e a t t h e a n g l e o f θ t h e n n e t f o r c e i s g i v e n b y : f = \sqrt{f 1^{2} + f 2^{2} + 2 f 1 f 2 \cos θ} h e r e θ i s n o t g i v e n, s o u \sin g t h e a b o v e e q u a t i o n w e c a n f i n d t h e n e t f r c w h e n θ i s g i v e n (2) d i r e c t i o n o f n e t f o r c e, m a k i n g a n a n g l e ϕ w i t h f 1, \tan ϕ = \frac{f 2 \sin θ}{f 1 + f 2 \cos θ} (3) w h e n o b j e c t i s n o t u n d e r t h e e f f e c t i f t h e s e t w o f o r c e s t h a t m e a n s, n e t f o r c e a c t i n g o n t h e o b j e c t i s z e r o . f = \sqrt{f 1^{2} + f 2^{2} + 2 f 1 f 2 c o s θ} = 0 f 1^{2} + f 2^{2} + 2 f 1 f 2 c o s θ = 0 400 + 900 + 1200 \cos θ = 0 \cos θ = \frac{- 12}{13} θ = \cos^{- 1} (\frac{- 12}{13})$

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