Falling objects | Physics | Khan Academy

If you drop a bowling ball and a feather in a room, the bowling ball falls first. No surprise, the feather just keeps floating over there. But if you could somehow create a vacuum chamber where there's absolutely no air in between and repeated the experiment, you'll find that both of them will hit the ground together. But why? Let's find out.

When we drop them in the vacuum, just after releasing them, what's going to happen? Well, for that, let's write down the forces acting on it. There is gravitational force acting downwards, and this force is, as we've seen in our previous video, given as mg, where m is the mass of the object and g is the acceleration due to gravity. Close to Earth, it's about 9.8 m/s².

Because the bowling ball has a much higher mass, you can see that I've drawn a much bigger arrow mark, so it has a stronger force of gravity compared to the feather. What other forces are acting on this? Well, there's nothing else. Remember, it's in a vacuum, so there are no air molecules over here, so no air resistance or anything. It's not in contact with anything else. This is it; this is the only force acting on it, which means this is the net force acting on our objects.

Now, whenever gravity is the only force acting on an object, we say that object is in free fall. So our bowling ball and our feather currently are in free fall. So what's going to happen? How will they fall? Well, to analyze that, we'll just use Newton's second law, which says that the net force acting over here should equal mass times the acceleration.

When you do that, look at what happens to their acceleration over here. The bowling ball's mass cancels out, and over there, the feather's mass cancels out, which means the acceleration of the bowling ball is g, and the acceleration of the feather is also g; it's exactly the same. Therefore, they will fall at the same rate. That's why they hit the ground at the same time.

But why did this happen? Think about it. I mean, a part of my brain is saying, but there is more gravitational force on the bowling ball—maybe 100 times more gravitational force on the bowling ball—then why didn't it fall faster? Ooh, because even though there's 100 times more gravitational force over here, there is also 100 times more inertia; it compensates. That's why the acceleration stays the same.

The beautiful thing about free fall is that they will always have the same acceleration, g, regardless of what their mass is. In contrast, when you drop them in air, the air molecules over here are going to hit the surface and start putting an upward force on them: the air resistance. Now, because along with gravity, there's also air resistance, it is no longer in free fall. Remember, you only say it's in free fall if gravity is the only force acting on them. Now there's also air resistance.

So how does that change things? Well, the first question I have for you is: we already know that the bowling ball falls faster compared to the feather. So can you think about which of the two has more air resistance—the bowling ball or the feather? Well, my intuition says, because the feather falls slower, maybe there's more resistance, so there's more air resistance over here. But let's see if this intuition is correct.

What does air resistance depend on? Well, it depends upon the surface area, because if there's more surface area, then more molecules can hit. It also depends upon the speed. If you're falling faster, you ram into these air molecules more—the impact would be more, and so the air resistance would be more. Now guess what? The bowling ball has a larger surface area and it is falling faster, which means the air resistance for the bowling ball is actually higher compared to the air resistance of the feather.

This arrow mark will be bigger compared to this arrow mark, meaning my intuition was wrong. But how does that make sense? If this has more air resistance compared to this one, then why does it end up falling faster? Well, the key is, don't compare the air resistance of the ball with the air resistance of the feather; instead, compare the air resistance with its own gravitational force.

In the feather, because the gravitational force is very small, the moment you drop it, within no time, as the speed of the feather increases, the air resistance will increase and very quickly it will immediately become equal to the force of gravity, and the net force over there becomes zero. From this point on, there is no longer an acceleration; the feather will just fall down pretty much at a constant velocity.

Now, the same thing happens for the bowling ball as well, but because the gravitational force is so big, even if it has a bigger air resistance compared to this one, look, it is not yet cancelled by the gravitational force. It'll take much more time for the air resistance to slowly become larger and then eventually balance it out, which means even right now, notice the net force is not yet zero. Since it takes more time for the air resistance to become larger and to cancel out gravity, this ball will accelerate much longer compared to the feather.

Therefore, it will pick up speed much quicker compared to the feather and it'll fall down and hit the ground first. Isn't that beautiful? So, long story short, when things are in free fall, meaning the gravitational force is the only force acting on them, then all objects will accelerate at the same rate, the acceleration due to gravity, regardless of their mass.

But if there are other forces acting on them, well then all bets are off; then we'll have to analyze. Now this particular fact has a very interesting consequence: it can give you weightlessness. That's right! You can be weightless even when there is a force of gravity acting on you. Let's see how.

Stand on a weighing scale. Now, there are two forces acting on you: gravitational force acting down on you and the normal force. The weighing scale is pushing up on you. Now, we might think that weight is this force, gravitational force, but that's not true. See, the weight is the force that you are putting on the weighing scale; that's literally what the weighing scale is reading—it's your weight.

But the force that you are putting on the weighing scale is exactly equal and opposite to the force that the weighing scale is putting on you, which means your weight is actually equal to—not the gravitational force, but actually, in general, equal to the normal force acting on you. Makes sense, right? Because that's equal to the force that you are pressing and pushing on the weighing scale from Newton's third law.

Now, because your acceleration is zero in this case, because you're just standing still, in that case, the two forces must be balanced. The normal force will equal the gravitational force, and therefore your weight equals the gravitational force. But that need not always be true. For example, what happens when you are in an elevator which is accelerating up?

Now, as the elevator accelerates up, the weighing scale pushes on you harder, and it increases that normal force acting on you. I mean, think about it: that's the only way you would get accelerated upwards, right? If the upward force is bigger than the gravitational force, then that's the only way you can get accelerated upwards. This also means your weight has increased; the reading of the weighing scale will increase, your weight will increase, you feel more weight—you feel being pressed more.

And so, right in front of your eyes is an example where your weight can be bigger than the gravitational force. Similarly, if you're accelerating down, the exact opposite thing happens, and your weight now can be smaller than the gravitational force. Now, because your weight can keep changing, the reading on the scale can keep changing. Some people like to use the word "apparent weight" to remind ourselves that gravitational force has not changed at all.

But I think the best way to avoid confusion is to not confuse gravitational force with weight. Think of weight and gravitational force as different things altogether. Anyways, now what happens in the extreme case where your elevator is in free fall? Well, if it's in free fall, then notice the normal force will be zero because when you are in free fall, gravity is the only force acting on all of this.

Gravity is the only force acting on the elevator, the weighing scale, and even you. So the normal force is zero; you will feel weightless. Everything inside will feel weightless. There's hardly any force, hardly any contact force between the two. Therefore, since you don't feel your weight at all, it'll feel like you're just floating over there.

So, look, right in front of your eyes, even though you have the same gravitational force as over here, because you're in free fall, because the elevator floor is going away from you at the same rate you are falling down, you don't experience any weight, and therefore you get weightlessness.

Now, so far in all the examples we considered free fall in which things are actually moving down. But guess what? You can also have free fall when things are moving up. How, you ask? Well, just take a tennis ball and throw it up. If we neglect the air resistance, then during this entire motion of going up and coming back down, the only force acting on it is the force of gravity, right? Which means for this entire motion, it was in free fall. Even during the upward motion, it was in free fall.

Now, I know it sounds wrong to think that the ball is freely falling even when it's going up, but remember the word "fall" over here refers to the fact that the ball is accelerating down. Since it's accelerating down, even though it's going up, it's slowing down. That's the reason it's slowing down, isn't it? So for this entire motion, the ball was accelerating down with the free fall acceleration rate g. That's why for this entire motion, the ball is in free fall.

Now, such objects, when you project them up, when you throw them up and then they go into free fall, we give a name to these objects; we call them projectiles. For example, a rocket is not a projectile because the gravitational force isn't the only thing acting on a rocket; there are thrust forces acting on them as well.

However, when we usually talk about projectiles, we think about stuff that is thrown at an angle. This is also a projectile because, again, it'll be in free fall once it's thrown up. The question is, how do we analyze the motion over here?

Now, it sounds pretty complicated, but here's a beautiful thing: the ball can be thought of as it's going forward and it is going up at the same time; that's why it ends up going like this. Now, the beautiful thing is that if you look at it upward motion, it's a free fall motion just like this one. But if you look at its forward motion, it's a motion with constant velocity.

Why? Because throughout the entire motion, the only force acting on it is the force of gravity—that is in the vertical. There are absolutely no other forces, which means there are no forces in the horizontal. And if there is no net force acting on an object, remember it goes with a constant velocity.

So projectiles have a constant velocity in the horizontal direction. When you put it together, you will get that familiar curve; it'll go like this in a curve, and that curve is called a parabola. What happens if you throw it faster? Well, you will have a bigger parabola; it will go higher up and it'll go farther away. The faster you throw, the higher it'll go and the farther it will fall.

But remember that Earth is round! So what if you throw it so fast that as the ball's path curves, even the Earth curves below it? What's going to happen then? That's a story for another video. Free falling is awesome!