Which ball will hit the ground first

It just doesn't seem right. Oftentimes we say, "But a bowling ball weighs more than a golf ball doesn't that mean gravity is pulling on it more? Well, there's a distinction to be made here.

The bowling ball has a greater mass, so there's more stuff for gravity to act on. In that sense, gravity is pulling on it more. But it still doesn't fall any faster. So it takes more force to move the bowling ball. And the bowling ball is also the one gravity pulls on more. 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.

For example, make air resistance significant, have an uneven floor, make it curve around the horizon see Newton's Cannon , move at relativistic speeds, and so on. These elaborations are interesting considerations, but the point of the original experiment is to demonstrate to a learner the independence of the dimensional axes. If the ball is thrown exactly horizontally, then it will hit the ground at the same time as the dropped one - but it will a lot further away from the thrower.

Where you are going wrong is in assuming there is a horizontal force. The force of throwing the ball imparts linear horizontal momentum to it, which is preserved until the ball hits the ground when it is converted into heat, or transferred to another object. Once the ball has been thrown and ignoring air resistance there is only 1 force acting on the ball: gravity. That is the only force that causes the ball to drop.

The hand can no longer impart any force, as the ball has left it. When you throw a ball, we are assuming that you are throwing it horizontally. This means you are giving the ball only horizontal velocity. Since vertical displacement, velocity, and acceleration are all the same, time has to be the same. However, all of this can only be true if air resistance is negligible, that is, there is no horizontal deceleration.

Neglect air resistance. The horizontal motion of the ball is independent of its vertical motion because the force of gravitation is acting perpendicular to the horizontal direction.

Since the vertical component of velocity is the same in both the cases, so the balls will hit the ground at the same time. When an object is in freefall, if we assume no air resistance is acting on the object, then the only force pulling the object down is the object's weight due to gravity. So, back to the bowling ball and the feather: The reason the bowling ball reaches the ground first is because air resistance has a bigger impact on the feather as it falls.

That air resistance slows the feather down while not having much of an impact at all on the bowling ball. But what happens if we eliminate air resistance? Watch this video to see what happens to the bowling ball and the feather when there is no air resistance.

You can see that, when air resistance isn't a factor, the bowling ball and the feather hit the ground at the same time! How does this conversation help us with constant acceleration equations?