Question

An object is moving to the west at a constant speed. three forces are exerted on the object. one force is 10 n directed due north and another is 10 n directed due west. what is the magnitude and direction of the third force if the object is to conitnue moving to the west at a constant speed

Answer 1

If we want the object to continue to move at constant speed, it means that the resultant of the forces acting on the object must be zero. So far, we have:
- force F1 with direction north, of 10 N
- force F2 with direction west, of 10 N
The third force must balance them, in order to have a net force of zero on the object.

The resultant of the two forces F1 and F2 is
$F_{12} = \sqrt{F_1^2+F_2^2}= \sqrt{(10 N)^2+(10 N)^2}= \sqrt{200}=14.1 N$
with direction at $45^{\circ}$ north-west. This means that F3 must be equal and opposite to this force: so, F3 must have magnitude 14.1 N and its direction should be $45^{\circ}$ south-east.