Why do brooms stand up? What is the scientific reasoning behind this?

Below, we will discuss the mechanics from the perspective of mechanics.

1. Origin

Last night's broomstick storm originated from a screenshot of unknown origin, below. That is, NASA says that this day (2.11) is a special day for Earth's gravity, the only day a broomstick can stand up.

In fact, it's clear at a glance that whether the broom can stand up or not has nothing to do with the special gravity of the Earth that NASA says it is. Anyone with a little knowledge of mechanics can understand that what makes a broom stand upright is the structure of the broom itself.NASA couldn't take it anymore and came out and said: this is just a basic object phenomenon that can be repeated every day.

In fact, there are now tons of parsed texts or videos throughout the web. Their explanation is the well-known reason: the center of gravity is at the contact surface. But this explanation is too crude. This explanation is, after all, only a summary of everyday life experience, far from rising to the level of theory.

2. Special gravity?

It is well known that the motion of the Earth is actually a bit complicated, with both rotation and spin going on at the same time. So, is the Earth in a special position on February 11th, which puts the gravitational force on the planet into a special state? First of all, February 11th excludes the effect of rotation, and the probability is that it is the gravitational influence of the Earth's rotation.

Here we must give the formula for gravity as follows. g is the gravitational constant, m and m are the masses of the two bodies, and r is the distance between them. This expression tells us that gravitational force is only related to MMR because G is constant.

For objects on Earth, such as brooms, their mass is constant. Therefore, the influences are m and R. The mass of the earth itself is constant, and the only possible influence is the gravitational pull of other celestial bodies, such as the sun and the moon. Whereas a broomstick is less than 1kg, the distance from the broomstick to the sun or moon is 108,000 miles, so their influence is negligible. Simply put, the gravitational pull of objects on Earth is governed by the Earth itself. This actually excludes the effect of rotation on gravity.

Also, the Earth is actually an irregular body, and the radius r is actually different at every point on the planet. Therefore, according to the formula for gravity, the same object will have a different value of gravity at each point. While the average radius of the earth is 6371km, the ups and downs of the earth's surface have little effect on the final gravity value. So far, we can judge that the Earth's gravity on February 11 is not special at all.

3. Equilibrium and Stability

Since there's nothing special about Earth's gravity, that means you can actually set up a broom at any time. So, I can't help but wonder, how does a broom stand up? Before we analyze this broom, let's briefly go over the basic mechanics. The picture above shows ? Balance? s technique. There is a group of people who are very sensitive to balance and can stack objects based on strange angles. It may seem impossible, but it actually fits the mechanics.

The so-called balancing is actually more than just the combined force of the objects being equal to zero, it is only one of the conditions. The other is that the combined moment of force is equal to zero, which is also a condition that must be met. When we usually say that an object is balanced, we only say that the two forces are balanced, which is inaccurate.

Equilibrium can be divided into three cases, as in the picture above. Obviously the first ball is unstable and will fall. While the second ball is stable and always returns to its original position. The third ball is balanced everywhere. The balancing technique shown above and the vertical broom are unstable balances.

4. Flat Broom Analysis

As others have said, one intuitive reason a broom can stand upright is that its line of gravity acts across the contact surface. But this is just an empirical summary, far from being a very deep theory of mechanics.

When the broom is upright, the forces are as shown above. It's simple, just gravity and ground support. With these two forces, the combined force and moment of the broom is zero, so it can remain in equilibrium.

The blue color in the picture above is the contact surface between the broom and the ground, and the fork inside is the line of action of gravity. The upward supporting force of the ground can only form a pair of moments that cancel each other out if the line of action of gravity is on the contact surface. If the line of action of gravity is on the outside, the moment formed by the upward force on the ground lacks another moment to balance it. This is the mechanical principle by which a broom cannot fail.

The center of gravity of the broom is therefore very important. The broom consists of a broom head and a broom stick, of which the broom head has a heavier mass. So when you stand up, the whole center of gravity is closer to the broom head. It is just enough to fulfill the requirement of the line of gravity action through the contact surface.

After understanding the principle, we then analyze the broom head. Because the broom head is, after all, relatively soft, can not intuitively support an upright broom. Ordinary broom heads are made of bristle-shaped plastic. Although it is thin, it has a certain rigidity, so that it can be cleaned with a certain amount of scraping power. The force on the bristles of a broom head is shown above. This slightly enlarged bristle actually slightly increases the contact area, which is better for balance. Thus, as long as the bristles of the broom head expand outward as a whole, rather than being recessed, then the broom can be easily erected.

5. Summary

The gravitational pull of a broomstick on February 11 is exactly the same as any other date, there is nothing special about it.

The reason for the equilibrium is that the broom can stand up (the combined force and moment are zero).

For a broom to be balanced, the bristles of the broom head must be upright or extend outward, not concave.