a particle moving with kinetic enrgy K makes a head on elastic collision with an identical partilce at rest.Find the maximum potential energy of the system during collision

Dear Student,

In a collision, a large force acts between two objects for a short time. Other forces acting on the objects may be considered negligible for that short time, so the momentum, P, of the system of objects is conserved. For two objects in one dimension

P_i = P_f  ⇒  m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f

where 1 and 2 represent the two objects, and i and f represent initial and final states (i.e., before and after the collision).

If the collision is elastic then the total kinetic energy, K, of the system is the same before and after the collision. (During the collision, kinetic energy may temporarily be stored as potential energy.) In other words, the change in kinetic energy, ΔK, is zero.

On the other hand, if the collision is inelastic then the kinetic energy of the system will not be the same before and after the collision. If a collision between two objects is perfectly inelastic then the two objects stick together (v_1f = v_2f) and there is a maximum kinetic energy loss. (In general, all the kinetic energy isn''t lost, since that would requirev_1f = v_2f = 0, which would be inconsistent with momentum being conserved.) Before coming to lab, you should find a general expression for the fractional kinetic energy loss, ΔK/K_i, for the special case v_2i = 0 which will be examined in these experiments.

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