PURPOSE

To learn about conservation of momentum and kinetic energy by studying different types of simulated collisions.

PROCEDURE

For each collision, note the momentum and kinetic energy of the balls before and after the collision. Then check to see if these quantities are conserved by comparing total values.

RELEVANT EQUATIONS
 

 1.            p = mv

        (momentum of a particle)

2.           p_tot = m_Av_A + m_Bv_B
 

    (total momentum = vector sum of individual momenta )

 
3.             KE = mv²/2

            (kinetic energy)

CONCEPTS TO KNOW

Momentum; kinetic energy; elastic collision; inelastic collision

DISCUSSION

In this experiment, you will verify through computer simulation the conservation principles stated above. They are: conservation of momentum (C of M) and conservation of kinetic energy (C of KE). In the case where two bodies collide and move along a straight-line path both before and after the collision, the conservation of momentum is simply expressed as:

Keep in mind that the vector nature of the velocities is important here. In motion along a straight line, the vector direction is indicated with a plus or minus sign. In addition, in some of the cases you will consider in this experiment, the masses are two identical gliders, so the two masses are equal, and we can call them both m. This fact simplifies the conservation of momentum equation considerably:

The other conservation rule applies only to collisions that can be termed elastic. This usually refers to the condition where no mechanical energy is lost to heat during the collision. If any or both of the bodies are permanently deformed, that is, any deformation that occurs during the collision does not "spring back", then the collision in inelastic and conservation of energy does not apply. The worst case scenario for this type of collision is called completely inelastic when the two colliding bodies stick together after the collision. The conservation of kinetic energy can be expressed in general as:

Using the conservation of momentum for any collision, and the conservation of kinetic energy in the elastic collision case permits us to determine one or more unknowns. Usually there are four variables, the velocities of the two masses both before and after the collision.

For example, in an elastic collision, with two independent equations (C of M and C of KE), if we assume that the initial velocities of the two masses are known, then algebra theory tells us that we can solve for the two remaining unknowns with two simultaneous equations. Therefore, we should be able to find the final velocities of the two masses in the general case.

Another example is the completely inelastic collision. Here we only can apply C of M and not C of KE, but we also are dealing with only three variables, since the velocities of the masses after the collision are the same (they stick together). Thus, if the two initial velocities are known, we can solve for the one remaining unknown, the final velocity of the composite body, using one equation.

The simulations are run under the Interactive Physics application, and are automatically brought up when the appropriate links are selected. Six types of simulated collision will be explored: