Air cushion track
The air cushion track is a virtual experiment for investigating elastic and inelastic collisions in one dimension. Two bodies move on an air cushion track and collide with each other and with the ends of the track. The initial speed and mass of the bodies can be set and the bodies can be moved to their starting position using the mouse. The mass, position, speed, momentum or energy of the individual bodies can be displayed. To examine the conservation laws, the total momentum or total energy is also displayed when momentum or energy is selected. In addition to frictionless movement, air friction and/or sliding friction can also be switched on. You can select whether all impacts are elastic, or the impacts between the bodies are inelastic or all impacts are inelastic. The friction force during the impact can also be selected. Thanks to these diverse possibilities, not only idealized movements can be investigated, but also those found in experiments or everyday life.
Operation
The initial speed and mass of the bodies are set using the sliders. The mouse wheel can be used for fine adjustment. The bodies can be clicked on and moved to their starting position by holding down the left mouse button. The "Start" button starts at the set initial speeds, "Stop" interrupts the movement and "Continue" continues the movement at the current speeds. The length of the track can be set via the window width. The "Strength of inelasticity" slider can be used to set the strength of the friction leading to inelasticity during an impact.
Numerical implementation: Newton's equations of motion are solved with 4th order Runge-Kutta (step size 10 µs). During impacts, a spring with a large spring constant(D=10000 N/m) is active over a short distance (1 cm). For inelastic impacts, a frictional force F=-a*v with (0<a<100</em> Ns/m) is taken into account depending on the setting. Air friction: The frictional force due to air friction is proportional to v2 and the frontal area of the body. For a body of 1 kg, the frontal area A=100cm2 is correspondingly smaller for a smaller mass, the cw value is 1, the density of the air is 1.2 kg/m3. Sliding friction is proportional to the mass of the body (coefficient of sliding friction µ=0.1).
Note: The total momentum of both bodies is not conserved when they collide with the wall, as the walls are rigid and can therefore absorb and release momentum at will. Only by including the entire earth could a closed system be realized in such experiments.