0

You drop an object. It lands before hitting terminal velocity. What does the velocity graph look like? Jump discontinuity or continuous? (ie: Does it instantly go from moving to not moving? Or does it "gradually" slow down, as molecules collide & shift, etc?) What about Newton's 3rd? Does the thing technically "bounce" many times?

There may be a difference between what humans can perceive vs. the reality of what is happening. I want to graph the reality of what is happening, even if it's not able to be measured.

enter image description here

JackOfAll
  • 135
  • I thought a lot of physics questions' answers depend on your assumptions... –  Oct 19 '16 at 16:16
  • 2
    B) In the real world an object doesn't just stop instantly. There is some bending/give in the materials so the duration of slowing down is finite so the slope is large but finite. –  Oct 19 '16 at 16:17
  • This also depends on whether it is an elastic collision or an inelastic collision. Regardless, I think that this may be better suited for Physics.SE instead of here. –  Oct 19 '16 at 16:25
  • No mathematical statement will ever capture the complete "reality" of what is happening; you just get better and better approximations. Discontinuity is a pretty good approximation for many purposes. A very steep slope, accounting for deformation, is better. But now do you want to take into account the different speeds of the molecules of the object, the molecules that fell off at some earlier time, the curvature of space, the discrete states of quantum particles, etc, etc? At some point the models are far too complicated to understand and you are still not done. – Nate Eldredge Oct 19 '16 at 16:43
  • More of collision dynamics energy dissipation than maths.. On impact if energy is large it is absorbed in fracture when new area is produced; if the energy is small , elastic waves friction and heat inside the body are produced. – Narasimham Oct 19 '16 at 17:20

2 Answers2

1

What you are trying to graph is not the reality, is a function that tries to describe reality. This can be done on more than one way. The more real you want the model, the more sophisticated it must be. When choosing a model, one makes assumptions to simplify the situation and make it possible to handle.

In this model in particular, there is one strong assumption: that the object analyzed behaves as one particle.

Here's one way to think about it: at the moment the object touches the floor, the floor begins to stop it. However, no matter how strong is the force stopping the object, it will be a finite quantity and in consequence a finite (dis)acceleration. So the velocity doesn't abruptly become zero but decreases fast until it reaches zero.

In any case, this depends on the model and physicists surely know better how to handle the question.

1

The world is continuous. No object can stop suddenly; there will always be a gradual change, all though small.

Newton's 3rd law says nothing against this. When dropping something on the floor, the thing falls and then suddenly (but gradually over a very short time interval) stops because of the normal force it feels from the floor. The floor feels the exact same force, which change over the impact duration.

The floor is not perfectly rigid, and so it might elastically bend a tiny bit. It might jump back elastically, as if the object fell on a trampoline, just in very tiny bounces, and so tiny oscillations can appear. But the amount of bouncing and oscillating depends on the damping of both object and floor: if the floor was a pillow or a thick carpet or alike, it would effectively stop all motion by becoming deformed during impact.

All in all, no classical physical motion behaves in discrete steps; the world is continuous.

Steeven
  • 50,707