Saturday, December 1, 2007

Answer to the BrainTeaser (and a cool thought experiment).

A week has passed. I guess its time to post the answer.

Dissidentman got it right.

The Answer is: The heavier the object, the faster the fall

Question of course is why?

When I was younger in physics class, I, and all other pupils besides, found it extremely puzzling why two objects would fall at the same rate once air resistance was discounted. The classic experiment being sucking the air out of two identical jars, and dropping a metal ball and a feather in them and observing the same speed and acceleration.

But heavier things are harder to lift. It just seemed so counterintuitive. School being school, we never got a good answer as to why.

Lets use Reductio Ad Absurdum to answer the puzzle. And to why the standard answer is wrong.
Acceleration due to gravity of earth is taken as 9.8 meters per second. Lets approximate this to 10. So a rock of mass/weight 1kg accelerates towards the earth at 10 meters per second. Following textbook logic - a rock of weight 5kg also accelerates at 10 meters per second.

How about a rock of a million kilograms? Still 10 meters per second?
10 million kilograms?
50 million?

Still the same?

Okay. How about a rock the same mass/weight/size/shape etc etc of the Earth itself? Here we arrive at the reductio that helps us solve the puzzle.

Obviously Earth attracts things towards itself at an acceleration of 10 meters per second. But the "Clone Earth" falling towards Earth will also attract the Earth towards itself at an acceleration of 10 meters per second. So the total acceleration will be 20 meters per second.

But this blasts out of the water the theory that all objects drop towards the earth at the same rate!

If my reading of history is correct Johannes Kepler was the first person to define gravity as the mutual attraction of two objects towards each other.

So how does that apply to the 10 pound and 20 pound objects? Simple.

We need to take into account the weight of the earth as well as the weight of the object. Say for illustration the earth weighed 10 thousand pounds.

The first object weighing 10 pounds falls as a function of the weight of itself and the earth, aka 10,010 (ten thousand and ten) pounds. While the second object falls as a function of a weight of 10,020 (ten thousand and twenty) pounds or about 0.1% faster.

In reality though the earth doesnt weigh 10,000 pounds - but trillions of pounds. So the slightly faster fractional speed that the heavier object falls at is so small as to be unmeasurable.

Still. Its a pretty cool thought experiment.