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Two forces of magnitudes 3N and 4 N act ...

Two forces of magnitudes 3N and 4 N act together on an object making an angle `60^(@)` with each other. Find the resultant force acting on the object.

Text Solution

Verified by Experts

Here `|bar(P)|=3N, |bar(Q)|=4N "and" theta = 60^(@)`
Let `bar( R) = bar(P) +bar(Q)`
Using law of cosines
`R = sqrt(P^(2)+Q^(2)+2"PQcos"60^(@))`
`=sqrt(3^(2)+4^(2)+2xx3xx4(1)/(2))`
`implies R = sqrt(37)`
Let `bar(R )` make angle `alpha` with `bar(P) ` Using law of sines
`(R )/(sin60^(@))=(Q)/(sinalpha)`
`implies sin alpha= (4xxsqrt(3))/(sqrt37xx2)`
`sin alpha= (2sqrt(3))/(sqrt(37))`
`alpha=sin^(-1)2(sqrt((3)/(37)))`
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