Question

Can a 20 N force and 40 N force ever produce a resultant with magnitude of 27 N?

Answer 1

Sure ,Let's find angle between forces

• Vectors be A and B and resultant be R

$\\ \sf\longmapsto R^2=A^2+B^2+2ABcos\theta$

$\\ \sf\longmapsto 27^2=20^2+40^2+2(20)(40)cos\theta$

$\\ \sf\longmapsto 729=400+1600+1600cos\theta$

$\\ \sf\longmapsto 729=2000+1600cos\theta$

$\\ \sf\longmapsto 1600cos\theta=-271$

$\\ \sf\longmapsto cos\theta=-0.169$

$\\ \sf\longmapsto \theta=cos^{-1}(-0.169)$

$\\ \sf\longmapsto \theta=80.2°$