Collisions in classical mechanics

In summary, classical mechanics only considers gravity as the main force, but problems involving collisions and friction are also important. These forces are intrinsically electrical and outside the scope of classical mechanics, but are often included in courses and can be treated as velocity-dependent forces. They may contradict classical mechanics at high speeds, but for everyday objects at slow speeds, they can be incorporated into classical mechanics without issues.
  • #1
stroustroup
14
0
The only force really considered in classical mechanics is gravity. And yet, we often have problems involving collisions and friction, which are intrinsically electrical phenomena, and thus outside the scope of classical mechanics. We have laws such as conservation of momentum which is used for collision problems, but in the end this is all based on the assumption that collisions obey Newton's laws (the 3rd in particular). Also, including collisions and friction basically means accepting the electrical force, and thus Maxwell's equations, which have been shown to contradict classical mechanics (galilean invariance vs lorentz invariance).

Including friction and collisons also causes the systems to be hard to describe using Lagrangian or Hamiltonian approaches (discontinuous potentials), which is another argument that they might be "out of place" in mechanics.

And yet, any course on mechanics has a section on collision problems and friction force. Can we really consider them as classical mechanics phenomena? How would the forces causing collisons be described in a consistent way with Newton's laws?

Would mechanics be consistent if we assumed collisions did not exist (i.e. objects pass through each other) and there was no friction? Even rigid bodies would not exist then...
 
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  • #2
I think you're reading too much into things... Classical Mechanics studies forces acting on everyday objects at slow speeds. Under these circumstances friction can be treated as a force that is velocity dependent and that's all you need to have theory match experiment.

Of course in a more advanced treatment can bring in EM theory but that now becomes an EM problem.
 
  • #3
You are right that the friction and collisions are (deep down) due to the EM force. The same holds for pressure and viscosity in fluids. But we care for the lorentz invariance only when the speeds are big enough and comparable to the speed of light. For low speeds there is nothing wrong to encompass these forces into the regime of classical mechanics.
 

1. What is a collision in classical mechanics?

A collision in classical mechanics is an event in which two or more objects come into contact with each other and exchange energy and/or momentum. This can occur between particles, such as atoms or molecules, or larger objects, such as planets or cars.

2. What factors determine the outcome of a collision?

The outcome of a collision is determined by several factors, including the masses and velocities of the objects involved, the angle and direction of the collision, and the elasticity (or "bounciness") of the objects. Inelastic collisions, where objects stick together after colliding, have different outcomes than elastic collisions, where objects bounce off each other.

3. How do we calculate the momentum and kinetic energy during a collision?

The momentum of an object is calculated by multiplying its mass by its velocity. During a collision, the total momentum of the system must be conserved, meaning that the sum of the momentums before the collision is equal to the sum of the momentums after the collision. The kinetic energy, or energy of motion, is calculated by using the mass and velocity of an object in the equation KE=1/2mv^2.

4. What are the different types of collisions?

There are three main types of collisions in classical mechanics: elastic, inelastic, and completely inelastic. In an elastic collision, both the momentum and kinetic energy are conserved. In an inelastic collision, only the momentum is conserved, and some kinetic energy is lost as heat or sound. In a completely inelastic collision, the objects stick together after colliding, and both momentum and kinetic energy are not conserved.

5. How are collisions used in real-world applications?

Collisions are used in many real-world applications, including car accidents, sports, and particle physics. Understanding and analyzing collisions can help engineers design safer cars and equipment, and can also provide insight into the behavior of atoms and particles. In addition, the study of collisions in classical mechanics is fundamental in understanding the laws of motion and energy conservation.

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