Vectors, The resultant of two forces 3P and 2P is R. If the first force is doubled then, Physics

Vectors, Physics

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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

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3/9/2013 5:23:12 AM case 1, R²=(3P)²+(2P)²+232P²cosΘ = 9P²+4P²+12P²cosΘ = 13P²+12P²cosΘ ----->(1) case 2, (2R)²=(6P)²+(2P)²+262P²cosΘ ; 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°

3/9/2013 5:23:12 AM

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°

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Vectors, Physics

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