Invisible Walls
Why does a ping pong ball hover directly over a straw when you blow under it?
Let's start by talking about equilibrium. In simple terms, an object is in equilibrium if all the forces on it are balanced. It has no acceleration. Now imagine we have a mountain range with hills and valleys. On the top of a hill and at the bottom of a valley, we place a ball (Figure 1). Our intuition explains what happens in each of these situations. If we push the ball on top of the hill to the side, it will roll down the side and leave its equilibrium spot. Conversely, if we push the ball in the valley to the side, it might roll back and forth a few times, but it will end up in its initial equilibrium spot. This ball on the mountain is in unstable equilibrium, and the ball in the valley is in stable equilibrium. An easy way to identify a stable equilibrium is by determining if the object will return to its equilibrium point after a slight push. Today's article is about the image in Figure 2. You might think that pushing the ping pong ball to the side a little would send it flying off in a different course. Instead, it returns to its original point. It is in a stable equilibrium.
Figure 1
Figure 2
We've simplified our question. To find out why the ball hovers directly over the straw without accidentally being blown away, we only need to know why it is in a stable equilibrium. Further simplifications can be made by looking at each direction. Vertically, gravity pushes down on the ball, and the wind pushes up on the ball, as displayed by Figure 3. If the ball is pushed down, the wind force is greater and will push it back up. If it is pushed up, then gravity pushes it back down. It's not hard to understand why the ball is in stable equilibrium vertically, but why doesn't the ball fall off to the side when pushed horizontally (like the ball on top of the mountain)? Our new question is why the ball is in stable equilibrium in the horizontal direction.
Figure 3
To answer this question, let's look at the wind that's pushing on the ball. Fluids are substances that can deform continuously by force. By this "physics" definition, the air and wind around us are all fluids. This means that the wind being blown on the ball is subject to the laws of fluid dynamics, creating some interesting implications. Firstly, the wind that is being blown has energy. It is important to note that the faster something moves, the more energy it has. Another property of fluids is pressure. Pressure is the force the fluid exerts on its surroundings divided by the area the force is exerted on. Bernoulli's Principle for fluid dynamics says that if you add the pressure and energy of a fluid in motion, it will always be the same. This implies that if energy is increased, the pressure must decrease to keep a constant sum. Recall that if something moves fast, it has more energy. Figure 4 is a diagram of the airflow around the ping pong ball, represented by dotted lines. Due to the ball's geometry, the wind (green highlight in Figure 4) that goes around the side of the ball moves faster than the air around it. This means that the wind going directly around the ping pong ball's left and right has more energy. More energy means less pressure, so the ball is effectively sitting in a spot of low pressure.
Figure 4
The ball is in an area of low pressure, which directly implies that it is in stable equilibrium. This is because pressure is directly proportional to force. In equilibrium, the pressure on both sides is the same, so the forces cancel out. Say we displace the ping pong ball a little bit to the right. Continue to reference Figure 4. The left side of the ball is still in the low-pressure zone. The right side of the ball is now in a high-pressure zone. The high-pressure zone on the right exerts a greater force than the low-pressure zone on the left. Therefore, after the ball is displaced to the right, it is pushed back into the middle. This explains why the ball stays in its place despite small fluctuations in different directions. It always gets pushed back to its stable equilibrium point.