Large ball and small ball 2 (same density)

Let's take a look!

What type of experiment is this?

Experimental procedure and explanation:

• Take styrene foam large balls (30 mm diameter, red) and small balls (6 mm diameter, white) having approximately the same density.
• Place the large balls (red) inside the container at the bottom and the small balls (white) on top.
• If you shake the container up and down, the positions will be reversed and the large balls appear on top.
• This is because the small balls enter the gaps between the large balls, and they are shaken, the number of balls passing through the gaps increase, and eventually all the small balls fall down. The large balls (red) end up on top, and the small balls (white) end up on the bottom.
• Next, drop the large and small balls into a container at the same time. The bigger balls will go down faster.
• This is a similar experiment to the previous “Large ball and small ball”, but the result is the opposite. In “Large ball and small ball”, large balls and small balls with the same weight were used in the experiment, and the small balls fell faster. Larger balls occupy a larger area that receives the fluid flow (frontal projected area), and the air resistance increases proportionally, causing the ball to fall slower.
• This experiment involved large and small balls with similar densities, and the large balls fell faster. Why is this?
• This is due to the nature of air resistance and gravity. The magnitude of air resistance varies depending on the shape, size, speed, etc., of an object. The magnitude of air resistance is roughly proportional to the area receiving the fluid flow (frontal cross-sectional area), so it is roughly proportional to the square of the size (length) of the object (e.g., if the size doubles, then the air resistance is about four times higher). This is the same case as with the air resistance in “Mysterious powder”.
• On the other hand, the magnitude of the gravitational force acting on a solid ball with uniform density is approximately proportional to the cube of the size (diameter) of the ball (e.g., if the size doubles, the magnitude of gravitational force is approximately eight times greater). In other words, a larger ball results in a considerably larger gravitational force. The gravitational force becomes much larger than the air resistance becomes larger. Therefore, among objects of similar density, the larger object (red in this experiment) sinks faster. This is the same case as with the speed at which the object sinks in “Mysterious powder”.

[Note]	I designed this experiment because there were many examples seen in high school physics textbooks where “small stones” and “small objects” were dropped. That is, I thought it was interesting that smaller stones are more susceptible to air resistance. It is dangerous with “large stones”. Additionally, it is important to note that the effect of air resistance is actually the opposite of what many people, including science teachers, may believe. A smaller object has less mass and therefore less gravitational force acting on it, but its air resistance is still proportional to the square of its size (or frontal projection area). As a result, a smaller object experiences a relatively larger effect from air resistance compared to a larger object with the same density. This is because the magnitude of the gravitational force acting on an object is proportional to the cube of its size, while the air resistance is proportional to the square of its size. If the size (length) of an object is doubled without changing its shape, then the air resistance will increase by approximately four times, but the gravitational force will increase by approximately eight times, making the effect of air resistance relatively smaller. The larger object will experience a smaller air resistance if the objects have the same density. For large stones, air resistance can be ignored, but very small sand particles (e.g., yellow sand) are affected by air resistance. As a result, their falling speed decreases, and they do not fall with uniform acceleration. This experiment demonstrates this fact. Small water droplets, such as raindrops and mist, are also significantly impacted by air resistance, and their slow falling speed confirms this.
[Keywords]	Drag, air resistance
[Related items]	Mysterious powder, Large ball and small ball, Force received from wind 1 (effect of size)
[Reference]	“Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, p. 72–75.

◀　Back Next　▶