Question

sum of two forces is 8 kg wt. the magnitude of resultant of two forces is 4 kg wt. and it is at right angles to the smaller force. find the forces.

Answer 1

Sum of two forces is $8\mathrm{kg}$ wt. the magnitude of resultant of two forces is $4\mathrm{kg}$ wt. and it is at right angles to the smaller force. find the forces.

Solution:

Let:

$F_{r} = 4kg$

$\alpha = 90{}^{\circ}$

$F_{1} + F_{2} = 8kg$

$F_{1} - ?$ $F_{2} - ?$

From triangle:

$F_{2}^{2} = F_{1}^{2} + F_{r}^{2}$

Write a system of equations:

$\left\{ \begin{array}{l} F_{2}^{2} = F_{1}^{2} + 4^{2} \\ F_{1} + F_{2} = 8 \end{array} \right.$

Solutions of system are:

$F_{2} = 5,F_{1} = 3$

Answer: $F_{2} = 5 \, \text{kg}, F_{1} = 3 \, \text{kg}$