Imagine two objects, One weighing twice the other. If you held these two objects up high, one in each hand, and then dropped them precisely simultaneously, which one would hit the floor first: the heavier one, the light one, or neither (land simultaneously)?
Intuition might well tell you that the heavier one should fall faster. In fact, in my usual knowledge survey in 1311 I find a number of answers that the heavier one falls faster, even twice as fast. Funny - that intuitive answer is wrong, and this is easy to prove.
A tennis ball weighs about as much as 25 dimes, so the weight difference is obvious. Get yourself a tennis ball; any regulation ball will do. A dime should be easy. Now write down a prediction about which will hit the floor first when dropped simultaneously. Also note your prediction about their relative speed of fall.
Now - do the scientific thing: "Do the Experiment." The experiment will either support your hypothesis or prove it wrong. Find a nice clear space to perform your drop. Hold the ball in one hand and the dime in the other. Grip each between thumb and a finger so you can drop them cleanly.Time to find out. Drop ball and dime simultaneously; they must be released together. Oberve them hitting the floor. Write your observation following your prediction. Was your prediction correct? How did the fall rates compare?
Repeat this experiment as many times as needed to convince yourself of the result, which will be both hitting the floor at the same time. The heavier one (the tennis ball) does NOT land ahead of the dime. Surprised?
Isaac Newton's laws of motion and gravity predict this outcome. First you have
F = ma
which relates force, mass, and acceleration. Add to this Newton's Law of Gravitation:
F = (G M1 M2)/r2.
Here G is the gravitational constant (6.67 x 10-11 N m2/kg2.
M1 is the mass of object 1, M2 is the mass of object 2, and r is the
distance between them (centers of mass). You can find G in almost any physics or astronomy text.
Let's take these two and combine them, making the assumption that inertial mass and gravitational
mass are the same. If they are ever found different, we'll know! Set them equal to each other.
F = (G M1 M2)/r2 = ma
Since we get to choose, let's make the "m" in "ma" be "M2" from the gravity law, giving
(G M1 M2)/r2 = M2a
Since we are talking about falling objects on Earth, M1 will be Earth's mass, M2
is the mass of the falling object, and "r" is the Earth's radius.
In "ma" the acceleration "a" we are talking is that of the falling object.
Now to solve it. Notice that we have an M2 on both sides of the equation. We can divide
both sides by that to get
(G M1)/r2 = a
Surprised? You can see tht Newton's laws of motion and gravity (which work!) predict that the
acceleration "a" experienced by the falling object depends ONLY upon Earth's mass and radius.
The mass of the falling object (M2) does not affect its acceleration.
This explains why the tennis ball and the dime fall at the same rate; their mass is not a factor.
Let's hear it for Physics!