The resultant of the two forces 3N and2N at an angle θ is doubled when first force in increased to 6N. Find θ?

1 Answer
Mar 7, 2016

θ=2π3 or 120

Explanation:

Formula for resultant force of two forces P and Q is given by R=P2+Q2+2P×Q×cosθ.

When two forces 3N and 2N are at an angle θ, value of the first resultant is R1 is given by

R1=N32+22+2×3×2×cosθ=13+12cosθ

When first force is increased to 6N, the resultant force R2 is given by

R2=N62+22+2×6×2×cosθ=40+24cosθ

As R2 is doubled

N40+24cosθ=2×N13+12cosθ or

40+24cosθ=4×(13+12cosθ)=52+48cosθ

Hence, 24cosθ=12 or cosθ=12

and θ=2π3 or 120