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In many cases, a force is applied to only a small part of a rigid body, yet all the particles of the body accelerate immediately. How do particles on which the force does not act directly "know" that they are supposed to accelerate? I know the answer probably involves the transmission of the applied force in some way but I'll appreciate a good explanation. Furthermore, the acceleration of the particles on which the force acts directly depends on the mass of the entire body and not the masses of those particles themselves. Why is this the case?

Qmechanic
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Toba
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    To clarify: Are you assuming that the effect of the applied force is transmitted immediately throughout the body and asking how that is possible? Or do you already know that the effect takes time to propagate through the body and are asking about the physics of how it propagates? – Chiral Anomaly Nov 01 '20 at 17:30
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    The strength of the chemical bonds between the molecules of the material holds the material together, and transmits the force from the point of impact to every other molecule in the material. This happens very fast but not instantaneously, first of all it takes at least the light travel time for the other molecules to "know" to start to accelerate, secondly each molecule has mass and the bonds between the molecules are somewhat "flexible" (think spring-mass-damper system) causing the force to travel as a wave through the material. – user9413641 Nov 01 '20 at 17:32
  • @Chiral Anomaly I know that no signal can be transmitted instantaneously. However it seems as if the particles move instantaneously, that was why I added that to the question. – Toba Nov 01 '20 at 17:53
  • @ Vinzent can you give a more detailed explanation of how exactly forces get transmitted, preferably in an answer? – Toba Nov 01 '20 at 17:54
  • @Toba I'm writing from my Phone right now, maybe when I get home.. – user9413641 Nov 01 '20 at 18:08

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Exactly because all portions of the body don't move instantaneously according to an applied force at a given point, that most of the noises of everyday life are produced.

The disturbance propagates as an elastic wave through the body as explained here

If the body will only vibrate for a fraction of second, but stay at rest, or will also move as a rigid body, it depends on the boundary conditions (static friction forces for example).

The cause of the vibration are atomic/molecular interactions in the solid. In a metal for example, the cloud of electrons hold the nuclei at its positions. Any attempt to increase or decrease the interatomic distance generates a restoring force as in a spring-mass system.

The vibration effect is normally only a transient that vanishes very quickly by damping, if the final effect in the rigid body is a translation, or a rotation around one of the axis of inertia.

Claudio Saspinski
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"Rigid body" is an idealization.

Bodies that are well approximated as "rigid" have high tensile strength, high elastic modulus and high speed of sound. In this construct, "high" relates to the scale and forces of the system in question.

In reality, there is no absolutely rigid bodies. The acceleration propagates by acoustic waves with the speed of sound.

A certain body may be regarder both as rigid and as non-rigid. Imagine a church bell - you may consider it rigid when planning on how to transport it from the bell workshop to the church tower top. You have to assume it is pretty much elastic and non-rigid when you have to understand how it rings.

(There is a traditional physics practice experiment where you hit two metal cylinders together at their bases and use an electronic timer connected to them in order to determine the speed of sound in the metal. Cylinders stay connected together for the duration of the impact and the impact duration is the time the acoustic wave travels to the free ends and returns back to the impact side.)

fraxinus
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  • I know that the force is somehow propagated, it is how that exactly happens that I don't understand. How do particles transmit the force to one another? Furthermore, the acceleration of the particles depends on the mass of the entire body. Why does the acceleration of the particles on which the forces act directly depend on the mass of the entire body and not the masses of those particles themselves? – Toba Nov 01 '20 at 18:06
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    Particles (atoms, ions, molecules, etc...) like to keep certain separation between themselves and resist when you try to separate them, as well as when you push them closer. This is called elasticity. On atomic level it is electromagnetic forces between atoms and their constituent particles, complemented by the Pauli exclusion principle for electrons. – fraxinus Nov 01 '20 at 18:37