Question

Why is it difficult to use the law of conservation of energy to calculate the effects of a collision?

Answer 1

Conservation of Energy only applies to Elastic Collisions. Conservation of Momentum applies to both Inelastic and Elastic Collisions

Explanation:

Elastic collisions by definition do not lose energy.
Inelastic collisions do lose energy to heat and vibration.

Inelastic collisions actually do conserve energy, but the loss of energy to heat and mechanical vibration is hard to calculate so the math equating energy before and energy after is hard to balance.