I am curious as to how forces move when a system is in motion. This was never fully explained in my physics classes at university. Let me explain:
I understand the Newtonian (classical) physics that there are equal and opposite forces in play. So when I am standing the force I am exerting on the ground due to gravity is balanced by an upward force from the ground. However, when I lift one foot (say the left foot) the force from my body is now transferred through the right foot. However, where did the upwards force that was under my left foot go?
I assume the upward force 'moved' to balance the increased force exerted by my right foot. I can understand that it general, except for one point. How did the upward force 'know' that it needed to move – and, secondly, where it needed to move to?
This same question can be applied to many dynamic situations of motion, such in a moving vehicle. (I can think of many other examples as well).
I had one physicist trying to explain it to me but, I admit, I lost his explanation when he went down the quantum mechanics rabbit hole. Is there a classical explanation as to how forces know when and where to move when a system is in motion?
Best Answer
Forces are not considered to move in the sense you describe. Basically, a force is not like energy. If you have energy in one location then it can be localized and tracked as it moves to another location. We call such quantities (locally) conserved. Force is not conserved. It can just appear or disappear as needed to satisfy the laws of physics.
This can be understood purely classically with no need to invoke quantum mechanics. Forces are simply governed by various force laws. In the scenario you mentioned the relevant laws are Newton’s laws, the law of gravity, and Hooke’s law.
Newton’s laws describe how forces act in general. In your scenario they require that the force that the force of the floor pushing up on your foot must be equal and opposite to the force of your foot pushing down on the floor. They also say that your acceleration is the sum of the gravitational force pulling down and the contact force pushing up (divided by your mass).
It sounded like you were already aware of those. The force law that you may not be aware of is Hooke’s law. He said that the force required to deform an elastic object is proportional to the distance you deformed it. When you stand on the floor it pushes you up, but you push it down. This leads to small deformations in both the floor and your shoe.
When you lift one foot up, the force does not move from one foot to the other. Instead, you simply deform the floor a little more under your other foot and by Hooke’s law that increases the force pushing up there.
If you are worried about how the floor knew to deform more, consider what would have happened if it didn’t. Then as the first foot was lifted up, the net force would no longer balance, so your other foot would begin to accelerate into the floor. Since the foot and the floor cannot occupy the same space this would push the floor down, thus deforming it. So regardless, it deforms.