Introduction 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 Drop Down Menu 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 DropDown Menu 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. hint: COM, for the equation of conservation of momentum hint: COKE, or the equation of conservation of kinetic energy Buttons Play Step Forward Reset have their usual meaning.
Interesting Fact This simulation has real and ideal collision simulator targeted for A level Physics education.
Acknowledgement My sincere gratitude for the tireless contributions of Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian, Félix Jesús Garcia Clemente, Anne Cox, Andrew Duffy, Todd Timberlake and many more in the Open Source Physics community.