Momentum  1D Collision Simulation

Momentum One Dimension Collision Model

The motion of a body of mass m and velocity v is described by a vector quantity known as momentum p where

p = m v

 When objects collide, whether trains, cars, billiard balls, shopping carts, or your foot and the sidewalk, the results can be complicated. Yet even in the most chaotic of collisions, as long as there are no net external forces acting on the colliding objects, one principle always holds and provides an excellent tool for understanding the collision. That principle is called the conservation of linear momentum which states that

 
The total momentum of a system remains constant provided that no external resultant force acts on the system

 
For two bodies colliding linearly, it is written mathematically as a vector equation

 
Total initial momentum = total final momentum

m₁.u₁ + m₂.u₂ = m₁.v₁ + m₂.v₂


If external forces (such as friction) are ignored, the total momentum of two carts prior to a collision (left side of equation) is the same as the total momentum of the carts after the collision (right side of equation).

Collisions are classified into elastic (or perfectly elastic), inelastic and completely inelastic.

 

There is also a concept of kinetic energy of a moving body is stated mathematically by the following equation:

KE1 = ½ m₁.v₁²



Main Simulation View
The simulation has 2 collision carts on frictionless floor and wheels.
Sliders

Explore the sliders allows varying the variables .

   * mass of cart ONE, mass_1, m₁ in kg
   * initial velocity of cart ONE, u₁ in m/s
   * mass of cart TWO, mass_2, m₂ in kg
   * initial velocity of cart TWO, u₂ in m/s

Radio Buttons
Allows for selecting what kind of collision is simulated.

A Perfectly elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed
A Perfectly Inelastic collision is defined as one in which conservation of momentum is observed but the colliding carts stick together after collision with kinetic energy loss

Checkboxes
show: velocity, for visualizing the velocity vector
plot momentum vs time graph, for different representation of data for momentum of cart 1, 2 and both.
plot kinetic energy vs time graph, for different representation of data for kinetic energy of cart 1, 2 and both.
paused when collide, for visualizing the change in the velocity u₁ and u₂ to v₁ and v2
fast simulation, for cases where the velocity are low and repeat learners can spend time more usefully collecting and analysing data.
hint: COM, for the equation of conservation of momentum
hint: COKE, or the equation of conservation of kinetic energy

Buttons
Play
Step Back
Step Forward
Initialize
Reset
have their usual meaning.
known bug is the Step Back button implementation, please fix it if you can and email me the improved source XML.


 
Credits:
The Momentum 1D Collision model was created by created by lookang using the Easy Java Simulations (EJS) version 4.2 authoring and modeling tool. An applet version of this model is available on the NTNU website . Shout our thanks to the Ejs community namely, Francisco Esquembre , Fu-Kwun Hwang and Wolfgang Christian for their professional learning community support. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: http://www.um.es/fem/Ejs/ and in the OSP comPADRE collection http://www.compadre.org/OSP/.