.
So far this thread has 3 puzzles going that have not been answered all right, or completely:
.
Which raindrops fall faster, the small ones or the large ones? <--- (The OP)
.
A baseball is tossed upwards into the air.
Which takes longer, its flight up or its drop back down?
.
A large stone is 100 times heavier than a small rock, but when dropped at the same time, they fall with the same acceleration (ignoring air resistance). Why doesn't the large stone accelerate faster? Is it because of its weight, its energy, its surface area or its inertia?
.
.
I'd be glad to post my solutions but I don't want to spoil anyone's fun!
.
The baseball goes upwards faster and falls back down more slowly, having lost velocity due to air resistance all the way up and down.
Therefore, since the distance traveled is the same up and down, it takes longer to drop back down than it does to fly up.
.
.
As for the two stones, common sense tells us that heavy objects should accelerate faster than lighter ones, but experimental science has proven this is not the case. Newton's second law of motion shows that acceleration is directly proportional to force (
weight in this case) and inversely proportional to mass. The equation (f=ma, force equals mass times acceleration) can be written as:
a = f/m
where a is acceleration, f is force and m is mass. The resistance to change in motion due to mass is called inertia. Therefore, even though a large stone may weigh 100 times more than a small rock, it has 100 times more mass (and so 100 times more inertia), so the two factors cancel out (100 / 100 = 1). The answer is weight and inertia which offset each other, make the two stones fall together.
.
In general, and ignoring air resistance, the acceleration of every falling body near sea level is 32 feet per second per second. If this experiment were tried at a greater elevation so the stones could fall for say, a mile or more, they would each achieve their respective terminal velocities, which would be faster for the larger stone and slower for the smaller stone, for the same reason
as explained in the raindrop answer (the square of the radius vs. the cube of the radius). In that case the surface area would become part of the answer, since half the surface area would be subject to air resistance, more precisely, the cross section area of each stone. But in this puzzle, that the two stones fall at the same rate is a given, and air resistance is specifically excluded.
Topic: PUZZLE -- Falling Raindrops (Read 5586 times)