Re: Mathematical model of inertia


"MobyDikc" <mobydikc@xxxxxxxxx> wrote in message news:1140475045.540617.216120@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Dirk Van de moortel wrote:
"MobyDikc" <mobydikc@xxxxxxxxx> wrote in message news:1140447956.172319.119380@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
MobyDikc wrote:
Can someone provide a mathematical model of inertia?


Let's try this.

Can someone provide the mathematical statement of "unless acted on by
an outside force an object in motion stays in motion and an object at
rest stays at rest."?


Next, can someone provide the work to use that math to answer the
following question.

There is a ball with a mass of 20kg moving toward a 5kg ball at 1 m/s.
At 0 seconds, the balls are 2 meters apart.

What is the state of the system at 3 seconds.

Show all the math involved to make that prediction.

Before collision:
World line of ball_1: x = v t
World line of ball_2: x = d
Total momentum: m1 v
Total energy: 1/2 m1 v^2
This setup satisfies the initial conditions that at t = 0
the distance between the balls is d.


This is lke a mathematical restatement of my initial conditions.

That is good, I understand that.

But what mathematical maneuver did you use to get from these initial
conditions to a collision event, below:


Collision event:
{ x = v t
{ x = d
giving
( x, t ) = ( d, d/v )


How did you determine from the initial conditions that a collision
would happen?

The two balls collide when they have the same x-coordinate.
In terms of analytic geometry you draw two lines on an x-t
diagram and find the point of intersection.
With algebra you solve the set of equations
{ x = v t
{ x = d
for x and t, in terms of the given values of d and v
This gives
{ x = d
{ t = d/v
or short
( x, t ) = ( d, d/v )

This is very basic analytic geometry.

Dirk Vdm


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