Question

Find the magnitude and direction of the resultant of two forces p and Q in terms of their magnitudes and angle Q between them.

Answer 1

 

P and Q are two forces acting at a point O; making an angle θ. They are represented by OA and OB. the diagonal OC of the parallelogram OBCA represents the resultant R.

Draw CD perpendicular to extended line of OA. In the right angle triangle ODC.

OC² = OD² + CD²

= (OA + AD)² + CD²

= OA² + 2OA AD + AD² + CD²

= OA² + 2OA. AC cos θ + AC²

R² = P² + 2PQcos θ + Q² v

From triangle ADC

AC² = AD² + CD² & \(\frac {AD}{AC}\)= cosθ 

Magnitude of the resultant

R = \(\sqrt {p^2+Q^2 + 2PQ.cos\theta}\)

To find the direction:

If a is the angle made by R with P, then from the right angled triangle ODC