Question

A, B and C are the three forces each of magnitude 4N acting in the plane of paper as

shown in Figure. The point O lies in the same plane.

i. Which force has the least moment about O? Give a reason.

ii. Which force has the greatest moment about O? Give a reason.

iii. Name the forces producing (a) clockwise and (b) anticlockwise moments.

iv. What is the resultant torque about the point O?​

Answer 1

Explanation:

(i) We know that,

Moment of force = Force × Perpendicular distance

Since the perpendicular distance of vector C is least from the point O, Vector C will have the least moment about O.

(ii) We know that,

Moment of force = Force × Perpendicular distance

Since the perpendicular distance of vector A is greatest from the point O, Vector A will have the greatest moment about O.

(iii) (a) Vector A and B will produce clockwise moments. Explanation: If the turning effect on the body is clockwise, Moment if force is called clockwise moment and it is taken as negative.

(b) Vector C will produce anticlockwise moment. Explanation: if the turning effect on the body is anticlockwise, Moment of force is called anticlockwise moment and it is taken as positive

(iv) Resultant torque about point O = sum of torques due to vectors A, B and C 

∴ Resultant torque about point O

= −(4 × 0.9) – (4 × 0.8) + (4×0.6) Nm

= − 3.6 – 3.2 + 2.4 = − 4.4 Nm

The negative sign suggests that the resultant torque is in the clockwise direction.