With two forces acting at a point, the maximum effect is obtained when their resultant is …

Question

With two forces acting at a point, the maximum effect is obtained when their resultant is $4$ N. If they act at right angles, then their resultant is $3$ N. Then the forces are:

Accepted Answer

Maximum resultant (forces aligned): $P+Q=4$. Right-angle resultant: $P^2+Q^2=9$.

$$(P+Q)^2=16=P^2+Q^2+2PQ=9+2PQ \implies PQ=\frac72$$

$P,Q$ are roots of $t^2-4t+\dfrac72=0 \implies t=2\pm\dfrac{\sqrt2}2$, i.e. $\left(2+\dfrac12\sqrt2\right)$N and $\left(2-\dfrac12\sqrt2\right)$N.

Solutions · 1