Question

A plastic ball in a liquid is acted upon by its weight and by a buoyant force. The weight of the ball is 3.1 N. The buoyant force has a magnitude of 9.2 N and acts vertically upward. An external force acting on the ball maintains it in a state of rest. Which is closest to the external force, including direction?


9.2 N, downward


9.2 N, upward


6.1 N, downward


6.1 N, upward

Answer 1

There are three forces acting on the ball:
- its weight W, of 3.1 N, directed downward
- the buoyancy B, of 9.2 N, directed upward
- the external force F

In order for the ball to be in equilibrium, the resultant of these three forces must be zero:
$B-W+F=0$
where I put a negative sign in front of the weight, since it is directed downward. If we solve it, we find:
$F=W-B=3.1 N-9.2 N = -6.1 N$
So, the external force has a magnitude of 6.1 N and its direction is downward, given the negative sign.