



The Elastic Collision experiment
An experiment in elastic 2d collision between disk A and disk B is shown below. The experimental results will be used to confirm the 3 conservation laws :
1. Conservation of Momentum
2. Conservation of Angular Momentum
3. Conservation of Energy
The elastic collision between the two identical disks A and B takes place in a plane. The force acting between the masses is magnetic repulsion. The table on which the collision occurs is frictionless for the purpose of the experiment.
The following clips show the collision (clip I) and the stroboscopic exposures of the collision (clip II) taken at time intervals




Center Of Mass
When momentum is conserved, the center of mass (c.o.m) is defined as
where mass m_{i} is at distance r_{i} from the origin.
Its velocity is constant
as can be seen from the following graphic (prepared directly from the measured positions at equal time intervals):
Let us now analyze this figure to demonstrate conservation of momentum:
Initial velocity of the first mass
and its angular momentum about O:
Initial velocity of the second mass:
ant its angular momentum about O:
Thus the total initial angular momentum in 0.
The final velocity vectors of both masses are parallel to their position vectors relative to point O and thus
Point O was chosen for convenience, as the angular momentum about it is 0.
Exercise: choose another point P and proove that the angular momentum is conserved about it. Use the data obtained from the stroboscopic pictures:
We can see that in the limits of experimental error the initial total energy equals the final total energy.
The velocity was obtained not by direct measurment, but by using the formula
meaning that the velocity in the nth interval is the length of this interval divided by the time it took the mass to travel it.
Conservation of Energy
The kinetic energy of each of the masses is calculated from their velocities. The potential energy is defined as the difference between the total energy and the kinetic energy:
The kinetic energy of both the colliding masses is:
(with a plus sign rather than the minus sign in the middle expression immediately below)






From these graphs a relation between the intermass distance and potential energy can be deduced. Assuming that the potential energy is a polynomial function of this distance, and plotting a loglog graph we obtain: