Why We Don't Fall Through The Floor
Why We Don't Fall Through The Floor
The simple answer to the question comes from Newton's 3rd law. We exert a force on the floor when we stand on it and so the floor pushes up on us with an equal and opposite force. This means there is no resultant force acting on us and so we neither get accelerated into the air nor accelerated towards the center of the Earth.
The next question is how does the floor generate this force? If you hold an object in your hand, the way you do it is by tensing muscles which requires energy. Floors are inanimate objects however. They cannot tense themselves deliberately and expend energy to stop us falling through them.
So how does the floor generate the force?
Pauli's Exclusion Principle
Pauli's Exclusion Principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. Electrons are fermions and so this principle applies to them. When we stand on the floor, the Pauli Exclusion Principle prevents the electrons in our feet or shoes from getting too close to electrons on the floor. This is because they are not allowed to occupy the same electron orbital. This means an electromagnetic repulsion between feet and floor is generated. This force pushes the ground down a little which causes it to deform slightly.There is a whole layer of atoms below the ones on the surface however and so the atoms on the surface will also be prevented from sinking too far down by the repulsive force. This means as the floor deforms, the force from the lower layer of atoms on the surface atoms increases. Eventually this force will be equal to the force from our weight and the floor will stop deforming. If the floor stops moving down then we also will stop moving down and so this is why we do not accelerate through the floor.
The forces are massive which is why we barely notice any deformation however x-ray diffraction patterns can provide evidence that this does actually occur.
Beam Theory
If the floor you are on is only supported at its ends, then a different explanation is required. The floor can be thought of as a beam. The way beams can be modeled is by having diagonal members in the middle of the beam with horizontal members aligning the top and bottom of it. All the diagonal members feed load into horizontal members and the forces on the diagonal members are constant. This means through the material, you get the same forces in the middle of the beam but the forces on the horizontal members increase as you move away from the load on the beam.We do not fall through the floor because the floor can produce tensions and compressions along the diagonal members and these zigzag from our feet to ends of the beam. The horizontal members have to feed the load from the diagonal members however and this load accumulates as you move away from the load. If the horizontal stresses then become to big, the floor breaks. This kind of break due to bending is much easier to break than by direct tension or compression.
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