Physics of a Particle Collision

[Philosophaie]

I have two point masses, m0 and mp, colliding (with no radii) in an Elastic Collision (no mass loss). One has initial velocity, V0i. The other has initial velocity, Vpi. How do I calculate the initial forces, Foi and Fpi then formulate the final forces, F0f and Fpf yielding the final velocities, V0f and Vpf.

 

[scottdave]

You cannot calculate Forces just this information, but you can calculate velocities. Try reading this http://230nsc1.phy-astr.gsu.edu/hbase/elacol2.html

 

[Philosophaie]

What other information do you nee to calculate Forces? Delta T?

 

[scottdave]

What other information do you nee to calculate Forces? Delta T?

Yes, but knowing it is elastic, and using the formulas from the link, you can find the velocities after the collision.

Remember that momentum and velocity are vectors. Note that energy is not a vector; it uses the magnitude of the velocity vector.

 

[Philosophaie]

What would the equations be for the Forces from the given initial and final velocities?

 

[scottdave]

For your situation, you should be able to use $$Force = \frac {dv} {dt},$$
So if you know the change in velocity, and the time it took to make that change, then you can find the force.

 

[George Jones]

@Philosohaie, are you familiar with Dirac delta functions.

In an idealized elastic collision, as a functions of time, velocities are step functions, and the derivative of a step function is a delta function. Hence, the idealized force is a delta function in an idealized elastic collision.

 

[scottdave]

In case you don't know (or for anybody else reading this), the delta function is a very large force acted over a very small time. Think of something like hitting a nail with a hammer. In an ideal situation, it would be approaching infinite force happening in a time, approaching zero.

 

[Philosophaie]

I think Force is F= dp/dt. For an Elastic Collision each momentum change from initial to final happens over a small time delta T. What I want to know is what the initial and final forces due to their velocities are so they can be summed to zero at the point of Collision.

 

[robphy]

For an impact collision [no interaction until contact], the initial and final forces are zero.
During contact, there is a nonzero variation of force-vs-time.
https://www.vernier.com/innovate/impulse-comparison-for-elastic-and-inelastic-collisions/

Have a look at the last force-vs-time graph for a collision on
http://stokes.byu.edu/teaching_resources/forcesensors.html (the graphs are equal because of Newton's Third Law and how the sensors are oriented)

Without details of how the collision occurs [e.g. position-vs-time data from https://serc.carleton.edu/dmvideos/videos/ball_re-bound.html ],
you can't get the details of how the force varies during the collision.
The best you can do is get a "time-averaged force" if you know the impulse and the interaction-time
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html