Vectors, Physics

The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. then the angle between the two forces us. plz xplain with the solution?
Ans)
r2=9p2+4p2+2.6p2cosθ....................1

4r2=(6p)2+4p2+2.12cosθ..................2

dividing 2 from 1

4=(36+4+24cosθ)/(9+4+12cosθ)

9+4+12cosθ=10+6cosθ

6cosθ=-3

cosθ=-0.5

θ=120degree

Posted Date: 3/9/2013 5:21:07 AM | Location : United States





case 1, R2=(3P)2+(2P)2+2*3*2*P2*cosΘ = 9P2+4P2+12P2cosΘ = 13P2+12P2cosΘ ----->(1)

case 2, (2R)2=(6P)2+(2P)2+2*6*2*P2*cosΘ ; 4R2=36P2+4P2+24P2cosΘ = 40P2+24P2cosΘ ------->(2)

Multiply (1) by 4; 4R2=52P2+48P2cosΘ ------>(3)

(3)-(2) gives, 0=12P2+24P2cosΘ

Therefore, cosΘ = (-1/2) => Θ = cos-1(-1/2) = 120°

Posted by | Posted Date: 3/9/2013 5:23:12 AM


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