11.2. Scalars and Vectors – ( 1 )

Two forces f₁ and f₂ of magnitude 5N each inclined each other at 60^o, act on a body. Find the resultant force acting on body.

The resultant force acting on body can be given by parallelogram law of vector addition

Statement –

If two vectors of same type starting from same point, are represented in magnitude and direction by two adjacent sides of parallelogram. Then their resultant vector is given in magnitude and direction by the diagonal of parallelogram starting from same point.

Mathematically,

R = √ { f₁² + ( 2 f₁ f₂ cos θ ) + f₂² }

R = √ { ( 5 ) ² + [ 2 ( 5 ) ( 5 ) cos ( 60 ) ] + ( 5 ) ² }        

As cos 60 = 1/2

R = √ { 25+ [ 50 ( 1 / 2 ) ] + 25 }

R = √ { 25 + 25 + 25 }

R = √ { 75 }

R = 8.66 N

The resultant force acting on body is 8.66 newton.