In simple vernacular, it means that the objects with light weight at the top and heavy weight at the bottom are relatively stable, that is, the lower the center of gravity, the more stable it is. So no matter how the tumbler "falls", it will always "get up" again. Let's see why the tumbler can't fall. Welcome to check it!
Why can't a tumbler fall
We all have this experience: flat bricks are very stable, and it is easy to overturn when they are erected; Half a bottle of water in the bottle is stable, and an empty bottle or a bottle full of water is easier to overturn. From the above two examples, to make an object stable and not easy to overturn, two conditions need to be met: first, its bottom area should be large; Second, its center of gravity should be low. The center of gravity of an object can be regarded as the acting point of the resultant force of its gravity.
For any object, if its bottom area is larger and its center of gravity is lower, it will be more stable and less likely to overturn. For example: tower buildings are always big at the bottom and sharp at the top; When shipping goods, always put the heavy things under and the light things on top.
With this knowledge, let's take a look at the tumbler. The whole body of the tumbler is very light, but there is a heavy lead or iron block at its bottom, so its center of gravity is very low; On the other hand, the bottom of the tumbler is large, smooth and easy to swing. When the tumbler tilts to one side, due to the change of the fulcrum (the contact point between the tumbler and the desktop), the center of gravity and the fulcrum are not on the same plumb line. At this time, the tumbler will swing around the fulcrum under the action of gravity until it returns to its normal position. The greater the inclination of the tumbler, the greater the horizontal distance between the center of gravity and the fulcrum, the greater the swing effect caused by gravity, and the more significant the trend of restoring it to its original position. Therefore, the tumbler can never be pushed down.
Like the tumbler, the original stationary object can automatically return to its original equilibrium state after being slightly disturbed, which is called stable equilibrium in physics. Spherical objects such as table tennis, football and basketball can continue to maintain balance at any position after being subjected to external force. This state is called random balance. For an object in random equilibrium, the center of gravity and fulcrum are always on the same plumb line, and the height of the center of gravity remains unchanged. The pencil placed horizontally on the table is a kind of random balance. No matter where it rolls, the height of the center of gravity remains the same.
The reason why the tumbler doesn't fall
The reason why a tumbler can't fall is that its whole body is very light, but there is a heavy thing (lead or iron) at its bottom. Therefore, its center of gravity is very low On the other hand, the bottom area of the tumbler is large, smooth and easy to swing When the tumbler tilts to one side, due to the change of the fulcrum (the contact point with the desktop), the center of gravity and the fulcrum are no longer on the same weight vertical line. At this time, the action of gravity will make it swing around the fulcrum and make the tumbler return to its normal position The greater the inclination of the tumbler, the greater the horizontal distance between the fulcrum and the center of gravity. The swinging effect produced by gravity will increase, and the more obvious the trend of restoring it to its original position. Therefore, the tumbler can never be pushed down
Related characteristics of tumbler
fractal structure
The tumbler is a hollow shell with light weight; The lower part of the body is a solid hemisphere with a large weight, and the center of gravity of the tumbler is within the hemisphere. There is a contact point between the lower hemisphere and the bearing surface. When the hemisphere rolls on the bearing surface, the position of the contact point will change. The tumbler always stands on the bearing surface with a contact point, and it is always a one legged body.
stability
When the tumbler is under the action of external force, it will lose its balance. After the external force is removed, the tumbler can return to the equilibrium state by itself, which shows that the tumbler has the ability to resist the interference of external force and maintain balance, which is the stability of balance. The formation of this ability to resist interference and maintain balance should be seen from the stress of the tumbler.
Stress condition
First, the force on the balance of the tumbler. On the table, the tumbler is affected by two external forces: one is gravity g, the attraction of the earth to the tumbler; The other is the support force, the reaction force of the desktop on the bovine sphere. According to the balance conditions of the object, as long as the two forces are equal in size, opposite in direction and act on a straight line, the tumbler can maintain a state of balance.
Second, the force on the tumbler tilt. When the tumbler tilts, it is affected by two torques. We call the action of external force interference, and the external force forms interference torque; The other is called resistance moment, which is formed by its own gravity. The tumbler was originally
Upright. Due to the action of external force, the external force produces torque on the contact point between the tumbler and the finished surface, making the tumbler tilt and breaking the original balance. In addition, the original gravity does not produce torque, because the original tumbler is upright, the action line and fulcrum of gravity are on the same straight line, and the torque is zero. Due to the action of external force, the tumbler tilts, the hemisphere rolls to one side, and the contact point moves accordingly to form a new contact point, that is, a new fulcrum. At this time, the action line of gravity is not on the same line as the original fulcrum, so a moment is formed, which is the resistance moment. It is precisely because of the formation and development of resistance torque that it resists and stops the interference of external forces. The direction of the resistance torque is opposite to that of the interference torque. At the same time, as the inclination angle of the tumbler increases, the offset of the action line of the center of gravity also increases, and the magnitude of the resistance torque also increases. When the resistance torque is equal to the interference torque, the tumbler enters a new equilibrium state - the inclined equilibrium state, and the interference effect of external forces stops. It can be seen that after the tumbler is disturbed by external forces, the original balance is destroyed, but a new balance is formed. The tumbler can continuously maintain balance. Although the ways of balance are different, the essence of balance remains unchanged. This is dynamic balance. Third, the stress of tumbler recovery. From the perspective of potential energy, the object with low potential energy is relatively stable, and the object will change towards the state with low potential energy. When the tumbler falls, the base that concentrates most of the center of gravity is raised, resulting in an increase in potential energy, so the tumbler should return to its original position. From the lever principle, when the tumbler falls, the action point of the center of gravity is always at the end. No matter where the fulcrum is, although the force arm of the base is short, the moment = force_ Arm, the tumbler will return to its original position because of the large torque at the other end of the base. In addition, the bottom of the tumbler is round and the friction is small, which is convenient for the tumbler to return to its original position.
In the whole process above, establishing a new balance is the main problem, because only in this way can we resist the interference of external forces, and restoring the original balance is a secondary problem, because the interference of external forces has been removed. In the whole process, the tumbler always maintains the attribute of balance, which is the "stability of balance".
Principle of mechanics
To sum up, the key point of this principle is to make the action line of gravity deviate from the fulcrum and make gravity produce torque on the fulcrum, that is, the resistance distance. As the tilting angle of the tumbler increases, the offset of the gravity action line increases, and the resistance torque also increases. Finally, the balance with the external force torque is realized. The ability of the tumbler to resist the interference of external force and maintain balance is formed in this way.
Introduction to the principle of tumbler
The upper light and lower heavy objects are relatively stable, that is to say, the lower the center of gravity, the more stable it is. When the tumbler is in balance in the upright state, the distance between the center of gravity and the contact point is the smallest, that is, the center of gravity is the lowest. The center of gravity always rises when it deviates from the equilibrium position. Therefore, the equilibrium of this state is a stable equilibrium. So no matter how the tumbler swings, he will never fall. Another example is the "cone rolling up" experiment we saw in the science and Technology Museum. Due to the shape of the cone and the shape of the tracks on both sides, its center of gravity is falling, but it seems to be rising. The upward rolling is inconsistent with the facts in life. But it is just a false image. Seeing its essence, the center of gravity is reduced, so the lower the center of gravity, the more stable it is. In order to increase the stability of objects in life, we often use to increase the weight below, such as fan base, microphone stand, bus stop sign, etc.
Using the feature of center of gravity, we can also do many interesting experiments and explain some phenomena. If you can be a weight worm, open a capsule and put it into a small ball, you can turn your head back and forth. We often put a box on the table only a little, but it doesn't fall down. This is because the box is close to one end of the table, which is the "center of gravity", so the box is suspended, but it doesn't fall down. The acrobat walking a tightrope holding a balance bar is also to reduce the center of gravity and achieve the purpose of balance. 1、 Principle of mechanics
The most common tumblers are the paper body and mud bottom, that is, they are molded with pulp or pasted with waste paper, and then made into a semicircular base with soil. After bonding the two, they are pasted with clean paper on the surface and painted with color; Some also use wood as the bottom, and iron blocks and small stones are fixed in the center of the bottom; There is also a "gourd" made of a small gourd with lead filled inside; Today, there are also small tumblers made of egg shells and old table tennis balls. All these tumblers have the same characteristics: the upper body is a hollow shell, the lower body is a solid hemisphere, and the bottom is round. These characteristics make them have a consistent basic mechanical structure and can achieve the effect of "no collapse".
Why can't a tumbler fall
No matter what, the lower the heavy end is placed, the larger the supporting surface is, the more stable it is and the less likely it is to fall. When the factory produces the tumbler, it always makes the lower part of the tumbler very heavy, and the bottom is made into a circle with a large area. So no matter how you push it, it will return to its original position and will never fall.
expand
The upper body of the inverted Weng is a hollow shell, which is very light; The lower body is a solid hemisphere with relatively large weight, so the center of gravity of the tumbler is within the heavier hemisphere below. There is only one fulcrum between the hemisphere and its bearing surface. When the hemisphere rolls on the bearing surface, the position of the fulcrum also changes. After careful observation, we can find that the tumbler always stands on the bearing surface with such a fulcrum, that is, it is always a one legged body.
Although it has one foot, without external force, its gravity and the supporting force of the ground are a pair of equilibrium forces with equal size, opposite direction and acting on a straight line, so it can maintain balance. So how does it keep its balance when there is an external force?
After receiving external force, the tumbler tilts and is affected by two torques, one is the interference torque of external force, and the other is the resistance torque formed by the tumbler's own gravity. According to the lever principle, when the tumbler falls, the action point of the center of gravity is always at the end, and no matter where the fulcrum is at this time, although the force arm of the base is short, the torque is large, so the tumbler will return to the original state, that is, the upright state, because of the large torque on the base. In addition, because the bottom of the tumbler is round, the friction is small, which is also convenient for it to return to its original state.
In this process, the establishment of a new balance is the top priority, because only by re establishing the balance can the influence of external forces be eliminated; Now that the influence of external force has been removed, it is no problem to return to the original state. The whole process, that is, the property that the tumbler always maintains balance, is called "stability of balance".
In simple vernacular, it means that the objects with light weight at the top and heavy weight at the bottom are relatively stable, that is, the lower the center of gravity, the more stable it is. So no matter how the tumbler "falls", it will always "get up" again.