Balanced and Unbalanced Forces

Children (and adults) associate the word balance with unmoving objects and, in the case of see-saws for example, they are right. They have great difficulty in seeing a falling parachute or watching a slowly sinking object as involving a balance of forces. This is where reiteration of the no net force no net change of movement idea must be made.

Let us consider the descent of a falling object:

In the first drawing, the object has just been released. Air resistance (the upward arrow) is low because the object has only just begun to accelerate and is moving relatively slowly at this point. Gravitational force (the downward arrow) will obviously remain constant throughout.

In the second drawing the object has been falling for a few seconds, accelerating all the time (getting faster and faster) because there is an imbalance between the gravitational force and air resistance (note the disproportionate arrow length). However, as the object travels faster and faster, there is a constant increase in the frictional force exerted by the air; notice how the upward arrow is now longer).

In the third drawing the object is still accelerating but the rate of acceleration is steadily being reduced as air resistance becomes greater and greater. In the final drawing the speed of the falling object is such that the force associated with air resistance is the same as that of the gravitational force. . . the forces are now balanced. At this point, the object stops accelerating and simply continues to fall at a constant velocity. This is called its terminal velocity.

Objects with a large surface area such as parachutes or sheets of paper reach terminal velocity much more quickly than objects with a small surface area because air resistance will have that much of a greater impact. Compare a falling sheet of A4 paper with a falling screwed up ball of A4 paper to see the impact of surface area.

One confusing aspect of all this is that a heavy parachutist falls more rapidly than a light parachutist which apparently contradicts the Gallilean idea that objects of dissimilar masses still accelerate to the ground at the same rate. It has to be remembered that while the air resistance on each parachutist is the same, the gravitational force on the heavy person is greater than that on the light person so in a falling situation, it takes longer for the heavy parachutist to reach terminal velocity and, as a consequence, will be falling at a faster rate.