Question

The greater and least resultant of two forces are 7N and 3N respectively. If each of the force is increased by 3N and applied at 60°. Find the magnitude of resultant

Answer 1

Let, magnitude of the two forces be F1 and F2.
given,
for greater resultant θ=0°
$\sqrt{ F1^{2}+F2^{2}+2F1F2cos0 }$
=[tex] \sqrt{(F1 +F2)^{2} } [/tex]
=F1+F2=7N            ...(i)
Now, for least resultant θ=180°
$\sqrt{ F1^{2}+F2^{2}+2F1F2cos180 }$
=$\sqrt{(F1 -F2)^{2} }$
=F1 -F2=3N             ...(ii)
Adding eqn. (i) and (ii) we get,
2F1=10 ; F1=5N
Puuting value of F1 in (i) we get,
F2=2N
After adding 3N to each force we get,
F1'=8N
F2'=5N
When they are applied at θ=60°
Resultant force F will be,
F=$\sqrt{F1' ^{2}+F2' ^{2} +2F1'F2'cos60 }$
After solving we will get,
F=$\sqrt{129}$N