How is force transmitted across a body?

Question

So I am leaning about various topics like physics like simple machines, center of mass, momentum, energy conservation, equilibrium but the more I study these "upper" level concepts the more I realize that I don't understand the very basic concept of force. Especially, graduating from the simplistic model of viewing objects as point particles to now examining them as objects with spatial dimensions (whether it might be symmetric or not), I have problem conceptualizing how (or whether even) force transmits through out the body of an object when it is specifically exerted only through one side of the body.

I know that mechanical force is possible b/c of electromagnetic reasons, so , let's suppose, if I have a object that is big and cube in shape and I happen to push that object with my hand touching the object on only one area (which is the area of the object that my hand happens to cover), can i assume that that the force that exert on only a certain area will travel to reach/influence all the other the other atoms making up the object no matter how far it is from the exact point of contact? Or will the force get weaker the farther other areas of the object is from the point of contact? If this way of thinking about force in physics correct or faulty?

This confusion specifically starts bothering me when I reach those other concepts like simple machines, static equilibrium, torque when there are multiple separate objects that are in contact with each other (like in of lever where you have seperate objects like fulcrum, lever, ground all touching each other or in static equilibrium you have things like wall, beam, ground all touching each other)and I now having trouble thinking how force diagrams work or why an object breaks under tension or how simple machines give mechanical advantage or how torque is possible etc... So if anyone can give their insight into this problem, that would be greatly appreciated. Thanks.

Answer 1

The answer depends on the material of the body you are exerting force on.

If it is a rigid body, then its shape is, by definition, constant. Assuming here for simplicity that your force vector passes through the COM, so that there isnt any torque on the body, then every particle will experience the same force in the direction you are pushing, as soon as you start pushing.

If the body is not rigid, like a sponge, then initially it will depress, as the areas closer to the point of application will recieve more force than others. The body will also simultaneously accelerate n the direction of force. This depression will continue till the restoring forces balance out the lesser of forces on the outer areas, till the steady state, when you see that the sponge, though a bit depressed at the point of application of force, is no longer changing its shape. In the steady state, the force on all of the particles is again, equal.

Practically, no body is truly rigid. However, in most objects that we term rigid, the depression is unnoticable, and the steady state is attained almost instantly.

Note: Check out this question, it might answer some more of your questions

Answer 2

Conceptualizing how force spreads out across an object is hard. This is why they pay mechanical engineers to analyze the results of supercomputers simulating how these forces behave. So don't be worried that it seems hard.

The tool I'd use to make sense of it all is the suspension spring of a car. We've dealt with them, so its a useful tool. If you push down on the car, it tries to push back up. If you try to pull up on the car, it pulls back down. The suspension spring is in a stable state. If you stretch it one way or the other, it resists that stretch.

The electrostatic bonds in solid objects are similar. At their rest state, they sit at a "natural" configuration. It's the one with the least energy stored in it. If you push on the object, the atoms on the surface are pushed on electrostatically and they "compress" the bonds behind. If you pull on the object, it stretches the bonds.

What may be tricky is to see how those forces get transmitted. Take this example. Find a decently long 2x4. Set each end up on blocks, and then stand on it in the middle. Obviously the force of you pushing on the 2x4 has to get transmitted several feet away to each of the supports. It has to, or you would fall. However, the way it does so is not straight forwrd. What you find is that you actually put the molecules in the bottom of the wood into tension. As you bend the 2x4, you make the bottom longer. Meanwhile, the top is in compression. As the molecules on the bottom stretch, they try to pull back inwards, and that puts a compression force on the molecules near the top. Thus, the force is being directed outwards towards the supports, but its using two very different mechanisms, a mere 3.5 inches apart!

For another example, I'd turn to Mr. Wizard's World, a TV show from the early '80s. He had a great example of this using salt. It's an example of just how counter intuitive forces can get when you have a great many particles all reacting to a force.