When you push an object, how much time does it take to start moving? [duplicate]

Imagine giving a quick gentle kick to a small wooden block resting on a frictionless table. It starts moving. I'm wondering if all the atoms/molecules of the wood start moving at the same time... I'm not sure if it takes some time for the atoms on the other side to feel the kick. I'm familiar with newton laws but I think newton laws treat the object as a point mass and don't really care about how the force is perceived by the atoms/molecules/lattice of the object. If possible I'm trying to have a simple explanation of how the force propagates from one side to the other side, and why the object starts moving in a straight line, instead of oscillating left and right or doing some other thing.

• Jul 17 '17 at 11:51
• The very simple answer is at the speed of sound. (ie, the speed of sound in that material.) This is my favorite "kid's physics question!" Jul 17 '17 at 12:42

If the body is elastic and you treat it as a continuum, then the deformation of the body is governed by the wave equation, involving the modulus of elasticity of the material and its density. See the following current thread: Solving a continuum-mechanical model At the end where you kick the object, you initiate a compression wave which travels through the object at the speed of sound in the material. Behind the wave front, the material is compressed and traveling a finite velocity. Ahead of the wave front, the object is still stationary, and traveling with zero velocity. The compressive strain behind the wave front is equal to the velocity divided by the speed of sound in the material.

• Perhaps a bit beyond the scope of this question, but what happens if you kick something and your 'shoe' is moving faster than the speed of sound? Jul 17 '17 at 11:56
• @DennisJaheruddin Simple answer: things break. Actual reality is a bit more complicated than that - most importantly, the speed of sound in a material isn't a constant. It depends on a lot of environmental conditions. A super-sonic jet doesn't actually travel above the speed of sound of the material (air) that immediately surrounds it - that material is denser and hotter, so it has a higher speed of sound. It only travels supersonic relative to the ambient air (which is what's usually meant by "supersonic flight"). In a solid, the same thing is usually followed by "things break" :) Jul 17 '17 at 12:51
• Good answer. Is it realistically possible to observe this phenomenon with a large object made of a material that conducts sound slowly? Jul 17 '17 at 13:18
• @DennisJaheruddin To further answer a natural continuation of that new question. Assuming you had arbitrarily strong materials with arbitrarily high speeds of sound in them, then the upper limit becomes the speed of light. The compression wave will never travel faster than the speed of light, and that's why you can't send signals faster than light by pushing a really long stick. Jul 17 '17 at 14:04
• @Luaan We are talking about a solid here. So the temperature of the solid has very little to do with the speed of sound in the solid, which is equal to $\sqrt{E/\rho}$. And, depending on the state of stress induced in the compression zone, the solid will or will not break. This can be quantified. Jul 17 '17 at 14:07

Atoms are bound together in a solid by being in perfect balance between repulsion and attraction forces - a bit further away, and they are pulled back in; a bit closer, and they are push back. This electromagnetic force between atoms propagates at the speed of light.

• Is the object perfectly rigid, then the only delay in the force transfer from particle to particle comes from these inter-atomic electromagnetic forces. The particles at the other side feel the push at the speed of light.

• Is the object elastic (or deformable), then energy is absorbed throughout. The force is then not transmitted fully but is damped and slowed down along the way (it is "spent" on moving particles rather than transmitted). Force is still transmitted between particles at the speed of light, but particles might move at much slower speeds before bumping into the straight-line neighbour.

• An elastic structure is for example a rubber band where curled-up chains of molecules are stretched out as if they were springs, which allows the whole material to elongate - the force is "spent" on stretching these chains.
• A deformable structure like a soft pillow might have large voids in-between particles. Force is again "spent" on moving particles around, in this case rearranging them permanently.
• "the only delay in the force transfer from particle to particle ..." From your first point, this describes the way sound travels in a substance. The speed at which the impulse travels will be the speed of sound for that material, not the speed of light. Jul 16 '17 at 22:37
• @StephenG If the material is perfectly rigid, then the speed of sound through it (basically vibrational motion) equals the speed of light. Naturally, no material is perfectly rigid, though. Jul 17 '17 at 7:45
• If it's perfectly rigid then there is no vibrational motion. Your answer implies both exist. I'd prefer you rephrased your first point to explain the impulse moves at the speed of sound due to these vibrations and forces and state the speed of light as an abstract limit if the interatomic bonds were perfectly rigid. Something like that would clarify the normal situation, IMO. Jul 17 '17 at 7:54
• @StephenG I do not mention vibration in the post. The term "perfectly rigid" should be enough explanation of this as an extreme / limiting case. Jul 17 '17 at 8:07
• ... just like there are no complete vacuums or perfectly elastic objects or stable equilibriums or ideal gasses. Ideal cases are still useful to understand as the limiting case Jul 17 '17 at 15:34

It is true that in solids the atoms and molecules of the lattice are held together in a quantum mechanical state which depends on electromagnetic fields and exchanges. Certainly this sets a limit to how fast a signal can travel in a solid. In metals, where electrons are shared by the whole lattice, the signal that an electron has been removed travels with the velocity of light through the metal.

But in a lattice with stable configurations of the atoms, connected with electromagnetic springs,an atom can only vibrate in its site location about a center, and transfer the energy vibrationally.

This has been studied using phonons

In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, like solids and some liquids. Often designated a quasiparticle,1 it represents an excited state in the quantum mechanical quantization of the modes of vibrations of elastic structures of interacting particles.

A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play an important role in many of the physical properties of solids, such as the thermal conductivity and the electrical conductivity. In particular, the properties of long-wavelength phonons gives rise to sound in solids -- hence the name phonon. In insulating solids, phonons are also the primary mechanism by which heat conduction takes place.

As a rule of thumb , the impulse/kick on a solid object will travel through its lattice at the speed of sound in that solid .

I would ask you treat this as a comment, as I don't have the rep to comment, and your question as a homework like question, so I won't answer directly

Look at the crystal structure of any solid object. Imagine the chemical bonds are, in effect, tiny springs. What will happen when you push on one side?

Look at Newton's Cradle motion on YouTube. Also, for liquids and solids, what happens over time, when you push them.

With these sort of questions, I find it best to imagine what is happening in really slowed down motion, like a bullet fired through an apple.

• Thank you, these questions are helping :) If the chemical bonds were like tiny springs, I guess the kick might propagate at the speed of sound ? Jul 16 '17 at 22:03
• I would leave out the speed of sound, it depends more on the "kick" or impulse you give the object, and actual material that the movement (hint) passes through. Unless you actually specify the speed of sound, it does not apply. I push my chair out of the way to vacuum under it, but not at the speed of sound. So don't just concentrate on the speed of sound, it's the impulse and the different springs tension that count.
– user163104
Jul 16 '17 at 22:10
• If you have done vectors, draw a free body diagram physicsclassroom.com/class. If you kick the block absolutely square on it, will follow a line in exactly the direction as you swing your leg, otherwise it will move offline. Newton's laws are vectors, they contain 3 directions.
– user163104
Jul 16 '17 at 22:12
• Yeah your reply is very helpful too, it get me thinking in the right direction. Thank you again :) Jul 16 '17 at 22:27
• @Hiiii How could it move in anything but a straight line (assuming perfect vacuum and absence of other forces etc.)? Things move in straight lines ("close enough") unless a force acts on them; they can "curve" as long as you keep the force on (while your foot is still in contact with the ball), but as soon as you stop applying the force, the object is back to a straight line. The object might also split into several disconnected pieces, each with its own straight-line trajectory, if you apply enough force. Jul 17 '17 at 13:02