When the marble is at the bottom of the container, its gravitational potential energy is minimal, so this point is a stable equilibrium point for it. stable equilibrium physics
Stable equilibrium is important for living beings and structures, that is why it is important to know what it depends on and how to maintain it.
By walking and executing movements, people and animals naturally maintain balance. Failure to do so will result in a fall. When practicing sports, stable balance is vital to develop the activity, such as playing soccer and running with the ball, preventing the opponent from taking it. stable equilibrium physics
Stability is so important in nature that people and animals have senses that allow them to know the position of their body at all times: proprioception. In the inner ear there are numerous receptors that transmit position information to the brain at all times.
Likewise, engineers and builders use the principles of stability to build structures capable of lasting over time and safe for users. Experience and the study of mechanics lead to establishing the following conditions to ensure the stable equilibrium of things:
Stable equilibrium in supported bodies
For a body to remain in stable equilibrium when supported, it must comply with:
-The body should have the largest possible support surface. This support zone is delimited by all possible axes with respect to which the object could rotate, overturning under the action of external forces.
The center of gravity should be in the lowest possible position.
Center of mass and bearing surface
The stable equilibrium of a body, animated or not, depends on the location of its center of mass, a very special point where all its mass is concentrated. Being on Earth, the center of mass coincides with the center of gravity, which is the point on the body where the weight is considered applied .
And it is that weight is one of the most important forces to take into account in the search for balance, since depending on how it acts, it can cause a torque or moment that makes the body rotate.
The center of mass does not necessarily contain mass. In a person standing or lying down, the center of mass is inside the body. But by bending to touch your toes without bending your knees, the center of mass is out. stable equilibrium physics
The other essential element to maintain the stable balance of an object is the support base or support surface. From experience it is recognized that objects with large bearing surfaces are more stable than those with smaller bearing surfaces.
To ensure that an object is in stable equilibrium, the perpendicular line connecting the center of mass to the ground surface has to pass through the base of support. If this line falls outside said base, the object will overturn.
Examples of stable equilibrium
To ensure the stable equilibrium of a supported object, these strategies are followed:
-Lower the center of gravity of the object, since the closer to the ground it is, the greater the stability. This can be achieved by making the lower body more massive.
-Increase the area in contact with the ground.
In the following figure there is a rectangular block made of homogeneous material supported on a horizontal surface. The center of gravity coincides with the geometric center of the block.
In the left image, the block is in stable equilibrium, since the perpendicular line that joins the center of gravity with the floor passes through the support surface, which is the base of the block. stable equilibrium physics
In the figure on the right, the block is inclined at an angle θ, in such a way that the perpendicular line that passes through the center of gravity falls just on the edge of the block. When the value of this angle is exceeded, the block tips to the right.
From the figure it can be seen that:
In case of overturning, the block would have a lower center of gravity, since a is less than b , and therefore, its position would be more stable, in addition to being supported on a larger surface.
Stable equilibrium situations
Common situations in which stable equilibrium participates, not just supported bodies, are described below: stable equilibrium physics
Pictures hanging on the wall
The pictures that hang from the walls are in stable equilibrium, without considering friction forces, but only the weight.
When a footballer runs after the ball or tries to prevent a rival player from taking it, he has to manage to keep his balance stable.
Stable balance is also very necessary when riding a bike or motorcycle.
It is known that stiletto-heeled shoes are not as stable as wide-heeled shoes, because they have a greater support surface than the former. stable equilibrium physics
When a person touches his toes with his hands, without bending his knees, the center of mass is outside the body. However, the person remains in a stable equilibrium, because the perpendicular line that connects the center of mass with the ground passes through the area delimited by the feet.
On the other hand, if the person tries to touch his toes, but keeping his back and legs close to the wall, he will see that he cannot do it without losing his balance, because the perpendicular that joins the center of mass with the floor does not pass by the area bounded by the feet. stable equilibrium physics
Ride the subway
To maintain balance when standing on a bus or train car, people immediately spread their feet. In this way the lift area is greater and it is less likely to fall.
Sports cars and racing cars use wide tires for greater stability.