Session 3 redux - The acceleration due to gravity

Tonight we're discussing the acceleration due to the ubiquitous force of gravity.

Contrary to popular belief, all objects do NOT experience the same force of gravity. An object experiences a gravitation force directly related to its mass. That is, greater mass equals greater gravitational force. All objects undergo the same acceleration (in the absence of air resistance) for a quite subtle reason. (Short answer: there is a greater attractive force of gravity for more massive objects; however, the greater force of attraction is offset by the greater inertia and resistance to motion. The two effects exactly cancel each other.)

Near the surface of the earth, the acceleration due to gravity (g) is:

g = 9.8 m/s^2

Which is to say, an object will accelerate (in free-fall) at a rate of 9.8 m/s^2 - increasing its speed by 9.8 m/s with each second of free-fall. Or, if it is rising, losing 9.8 m/s with each second of upward motion.

So, after 1 second of free-fall, the object will attain a speed of 9.8 m/s.

After 2 seconds, 19.6 m/s.

After 3 seconds, 29.4 m/s.

And so on.

Galileo's odd numbers rule was also discussed in class. Galileo determined that accelerating objects fall (or roll) through total displacements that are proportional to the amount of time squared. If we approximate g as 10 m/s^2, then:

x(1 sec) = 5 m

x(2 sec) = 20 m

x(3 sec) = 45 m

x(4 sec) = 80 m

Note that these displacements are proportional to 1, 4, 9, 16 - perfect squares. And interestingly, the differences between these "base" displacements are 1, 3, 5, 7...... odd numbers. Neat, eh?