Notes - Momentum and Collisions.pdf

Momentum and Collisions During a collision momentum is conserved assuming that the system is an isolated system. The system is isolated when there are no outside forces acting on the objects in the system. Completely Inelastic Collision – the two objects co...

Momentum and Collisions During a collision momentum is conserved assuming that the system is an isolated system. The system is isolated when there are no outside forces acting on the objects in the system. Completely Inelastic Collision – the two objects collide and stick together becoming one object. Therfore... vaf = vbf and the conservation of momentum becomes: mavai + mbvbi = (ma + mb) vf Elastic Collision – the two objects collide but do not stick together. mavai + mbvbi = mavaf + mbvbf Completely Elastic Collision – momentum is conserved AND kinetic energy is conserved. mavai + mbvbi = mavaf + mbvbf KEai + KEbi = KEaf + KEbf Combining the conservation of momentum and the conservation of kinetic energy we can derive a second equation for completely elastic collisions: Conservation of Momentum Conservation of KE mavai + mbvbi = mavaf + mbvbf ½ mavai2 + ½ mbvbi2 = ½ mavaf2 + ½ mbvbf2 Rearrange Conservation of Momentum Rearrange Conservation of KE ma(vai – vaf) = mb(vbf - vbi) ma(vai2 – vaf2) = mb (vbf2 - vbi2) Expand Conservation of KE ma(vai – vaf) (vai + vaf) = mb (vbf - vbi) (vbf + vbi) Divide Conservation of KE by Conservation of Momentum ma(vai – vaf) (vai + vaf) = mb (vbf - vbi) (vbf + vbi) ma(vai – vaf) = mb(vbf - vbi) Therefore... vai +vaf = vbi + vbf To solve collision problems, set up a table and then determine which collision is occurring. Object A Object B 1 – Completely inelastic then Mass (kg) 2 – Elastic, one equation so can only solve for _______ unknown Vinitial (m/s) 3 – Perfectly elastic, two equations so Vfinal (m/s) can solve for ______ unknowns Odd  Page  –  Create  a  venn  diagram  showing  the  similarities  and  differences  among  inelastic   collisions,  elastic  collisions,  and  perfectly  elastic  collisions