ACT Science: Conservation of Momentum—Elastic and Inelastic Collisions

Momentum p=mv (mass × velocity). In a closed system, total momentum before a collision equals total momentum after. Law: m₁v₁+m₂v₂=m₁v₁'+m₂v₂' (unprimed = before, primed = after). Elastic collision: kinetic energy is conserved (objects bounce apart). Inelastic collision: kinetic energy is not conserved; objects stick or partially deform (but momentum is still conserved). Key insight: momentum is always conserved; kinetic energy is conserved only in elastic collisions. This distinction separates the two collision types.

Intuition: A moving train and a stationary car collide. Before: total momentum is train's momentum + 0. After: they move together (inelastic) or separate (elastic). Momentum doesn't change; energy does.

Type 1 (Inelastic—objects stick): Car (m=1000 kg, v=10 m/s) hits stationary car (m=1000 kg, v=0). They stick. Find final velocity. m₁v₁+m₂v₂=m₁v₁'+m₂v₂' → 1000(10)+1000(0)=(1000+1000)v' → 10000=2000v' → v'=5 m/s. Type 2 (Elastic—objects bounce): Two balls, m₁=2 kg, v₁=6 m/s and m₂=3 kg, v₂=0. They collide elastically. Calculate final velocities (requires two equations: momentum + kinetic energy conservation). For elastic collisions: v₁'=((m₁-m₂)/(m₁+m₂))v₁ and v₂'=(2m₁/(m₁+m₂))v₁. v₁'=((2-3)/(5))6=-1.2 m/s (ball 1 rebounds). v₂'=(4/5)(6)=4.8 m/s (ball 2 moves forward). Inelastic collisions are easier because objects move together; elastic require both momentum and energy equations.

Test questions typically ask for final velocity (inelastic) or to identify collision type (elastic vs. inelastic).

Problem 1 (Inelastic): Two trucks (m₁=5000 kg, v₁=15 m/s) and (m₂=3000 kg, v₂=0) collide and stick. Final velocity? 5000(15)+3000(0)=(8000)v' → v'=9.375 m/s. Problem 2 (Identify type): Before collision, total KE=500 J. After collision, total KE=480 J. Type? Since KE decreased but the problem says it's a collision (momentum conserved), it's inelastic. Problem 3 (Momentum check): Ball A (2 kg) moving 10 m/s hits ball B (3 kg) at rest. After inelastic collision, they move together at 4 m/s. Verify momentum conservation: Before: 2(10)+3(0)=20 kg·m/s. After: (2+3)(4)=20 kg·m/s. ✓ Conserved. Complete all three daily for one week until you quickly identify collision types and apply conservation laws.

Remember: momentum is always conserved; kinetic energy is only conserved in elastic collisions.

Collision and momentum questions appear in 1-2 ACT Science passages. They are conceptual-plus-computational: understand conservation laws, then plug numbers into equations. Once you know momentum conservation and the difference between elastic and inelastic, these questions become predictable. Investing 20 minutes in this topic yields 1-2 guaranteed points because the concept is simple and formulas are provided.

Master momentum conservation one day before the test. On test day, you will answer collision problems with confidence.