Who said objects fall at the same speed

Oh, just in case you don't have ball experience—the bowling ball is MUCH more massive than the basketball. Maybe they hit the ground at the same time because they have the same gravitational force on them? First, they can't have the same gravitational force because they have different masses see above. Second, let's assume that these two balls have the same force. With the same force, the less massive one will have a greater acceleration based on the force-motion model above.

Here, you can see this with two fan carts. The closer one has a greater mass, but the forces from the fans are the same. In the end, the less massive one wins. No, the two objects with different mass hit the ground at the same time because they have different forces.

If we put together the definition of the gravitational force on the surface of the Earth and the force-motion model, we get this:. Since both the acceleration AND the gravitational force depend on the mass, the mass cancels. Objects fall with the same acceleration—if and only if the gravitational force is the only force. The gravitational field is not constant.

I lied. Your textbook lied. We lied to protect you. We aren't bad. But now I think you can handle the truth. The gravitational force is an interaction between two objects with mass. For a falling ball, the two objects with mass are the Earth and the ball. The strength of this gravitational force is proportional to the product of the two masses, but inversely proportional to the square of the distance between the objects.

As a scalar equation, it looks like this. A couple of important things to point out since you can handle the truth now. The G is the universal gravitational constant. It's value is super tiny, so we don't really notice the gravitational interaction between everyday objects.

The other thing to look at is the r in the denominator. This is the distance between the centers of the two objects. Since the Earth is mostly spherically uniform in density, the r for an object near the surface of the Earth will be equal to the radius of the Earth, with a value of 6, kilometers huge. So, what happens if you move 1 km above the surface of the Earth? The r " goes from 6, km to 6, km—not a big change. Even if you go ALL the way up to the altitude of the International Space Station orbit km , there isn't a crazy huge change.

Here, I will show you with this plot of gravitational field vs. Oh, and here is the python code I used to make this —just in case you want it. For just about all "dropping object" situations, we can just assume the gravitational force is constant.

OK, now we are getting into the fun stuff. What if you drop an object and you can't ignore the air resistance? Then we have a more complicated problem, because there are now TWO forces on the falling object.

There is the gravitational force see all the stuff above , and there is also an air resistance force. As an object moves through the air, there is a force pushing in the opposite direction of motion. This force depends on:. The part that makes this complicated is the dependency of the air resistance on the speed of the object. Let's consider a falling object with significant air resistance.

How about a ping-pong ball? When I let go of this ball, it is not moving. This means there is zero air resistance force and only the downward gravitational force.

This force causes the ball to increase in speed in the downward direction —but once the ball is moving, there is now air resistance force pushing up. This makes the net force a little bit smaller, and thus you get a slighter increase in speed. Eventually the air drag and gravitational force have equal magnitudes. The ball then falls at a constant speed—this is called terminal velocity. Since the net force on a falling object with air resistance isn't constant, this is a pretty tough problem.

Really, the only practical OK, not really the only way to model this is with a numerical calculation that breaks the motion into tiny steps during which the force is approximately constant. How about a model of a falling ping-pong ball?

Here you go. Click the pencil icon to see and edit the code, and click Play to run it. View Iframe URL. You can see that the ping-pong ball almost reaches a constant speed after dropping a distance of 10 meters. I put a "no air" object in there for reference. If you want to see what happens if you change the massgo ahead and change the code and re-run it.

It's fun. Now we get to the interesting question. If I drop two objects from the same height, does the heavier one hit the ground first? The answer is "sometimes. Drop 1: A basketball and bowling ball. He says the lighter ball always started out a little bit faster than the heavy ball. Then the heavy ball caught up. That sounds crazy. An assistant held four-inch iron and wooden balls at arm's length -- as Galileo would have to have held them to clear the wide balustrate atop the Pisa tower.

It turns out that when you try to drop them both at once, your strained muscles fool you. You consistently let go of the lighter one, the one you've been gripping less intensely, first. That means Galileo accurately reported what he seen happening. And we're left with no doubt that he actually did do the experiment. Galileo went on to become the first real challenger of Aristotle. His tower experiment was no fable -- no apple falling on Newton's head.

This was one of the first controlled scientific experiments. Like most of today's experiments, it was imperfect. But this experiment changed Galileo, and it changed history.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work. Photo by John Lienhard. The remarkable observation that all free falling objects fall with the same acceleration was first proposed by Galileo Galilei nearly years ago. Galileo conducted experiments using a ball on an inclined plane to determine the relationship between the time and distance traveled.

He found that the distance depended on the square of the time and that the velocity increased as the ball moved down the incline. The relationship was the same regardless of the mass of the ball used in the experiment. The experiment was successful because he was using a ball for the falling object and the friction between the ball and the plane was much smaller than the gravitational force. He also used a very shallow incline, so the velocity was small and the drag on the ball was very small compared to the gravitational force.

The story that Galileo demonstrated his findings by dropping two cannon balls off the Leaning Tower of Pisa is just a legend.