SNHS Physics Blog 6: Free Fall

Yunhui Shim

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When we step from a diving board to drop into the pool, air resistance has very little effect on the motion. In fact, our motion is very likely determined by the force of gravity. When an object is determined by the gravity force alone, this is referred to as the free fall of an object. When Galileo Galilei dropped objects from the leaning tower of Pisa, he concluded that if the effects of air resistance can be neglected, all objects in free fall will have the same constant acceleration. All objects, regardless of the size or weight they carry will be identical, provided that the air resistance is small enough to ignore. It is easy, today, to verify his assertions by dropping objects through a vacuum chamber. A very novel version of this experiment was carried out in the Moon, when an astronaut dropped each a feather and a hammer and found that they fell at the same time.

Air resistance is very easy to observe. For instance, when we drop a sheet of paper and a rubber ball at the same time, the paper drifts very slowly to the ground. However, once the paper is wadded together and the experiment is repeated, the time that the rubber and paper ball take to reach the ground is approximately the same. In general, the motion of an object can be treated as a free fall whenever the effects of resistance are small enough to be ignored. When the air resistance or other forms of friction are significant, the motion of the falling object is able to deviate from the ideal behavior of free fall.

Free fall can’t always be assumed as an object falling down. A thrown ball at any direction for instance does not affect its acceleration. It doesn’t matter if the ball is thrown upward or downward, or if it is simply dropped. The ball, when released from one’s hand is in free fall. The ball’s acceleration is caused by gravity and this acceleration produced the same downward acceleration regardless of how the ball moves. The acceleration due to gravity can be denoted as g and this acceleration due to gravity differs slightly from locations on Earth and the altitude above the surface. In all of the calculations we use, g=9.81 m/s^2 is for the acceleration die to gravity, and when we choose a coordinate system in which the positive direction is upward, the acceleration in free fall becomes a=-g.

The velocity of an object that is dropped from rest increases by the same amount with each passing of second, but the position of it changes more. Velocity increases linearly with time, in a linear relationship. Distance increases with t^2, in a parabolic relationship. The motion of an object also has a symmetry to it. The symmetry of a free fall can be seen in the position time graph.