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PURPOSE

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

EQUIPMENT  linear air track, DataLogger interface, gliders, two photogates, and weights.

RELEVANT EQUATIONS

Momentum of a particle:   p = mv

Total momentum = sum of individual momenta:   p_tot = m_Av_A + m_Bv_B

Kinetic energy:   KE = mv²/2

DISCUSSION

In this experiment, you will verify in practice the conservation principles studied previously in the collision simulation lab. 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:

An illustration of an elastic collision between two pucks is shown in this movie. Using the conservation of momentum for any collision, and the conservation of kinetic energy for an elastic collision 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.