In a 1D elastic collision, a 2 kg object moving at 6 m/s collides with a stationary 2 kg object. What happens after the collision?
ABoth objects move at 3 m/s — they share the initial momentum equally
BThe first object continues at 6 m/s; the second stays still
CThe first object stops; the second moves at 6 m/s
DThe first object bounces back at 6 m/s; the second stays still
Equal-mass elastic collisions result in complete velocity exchange: the incoming object stops and the stationary one moves off at the original speed. This conserves both momentum (m×6 = m×0 + m×6) and kinetic energy (½m×36 = ½m×0 + ½m×36). Option A conserves momentum but not kinetic energy (½m×9 + ½m×9 ≠ ½m×36). Options B and D both violate momentum conservation.
Question 2 Multiple Choice
A bowling ball (very large mass) rolls elastically into a stationary ping-pong ball (very small mass). Which outcome best describes what happens?
AThe bowling ball stops; the ping-pong ball moves forward at the bowling ball's original speed
BThe bowling ball barely slows; the ping-pong ball moves forward at roughly twice the bowling ball's speed
CBoth balls rebound in opposite directions with equal speeds
DThe bowling ball slows to half its speed; the ping-pong ball moves at three times the original speed
When m₁ >> m₂, the heavy object barely slows (its momentum is so large the light ball's reaction barely affects it) and the light ball launches forward at approximately twice the heavy ball's original speed. Option A describes the equal-mass case; option C would require zero net momentum initially, which is not the case here; option D overstates both the slowdown and the launch speed. These mass-ratio limiting cases are the key physical intuition anchors for collision analysis.
Question 3 True / False
The relative velocity of approach equals the relative velocity of separation in any elastic collision.
TTrue
FFalse
Answer: True
This elegant result follows from combining the momentum conservation equation (linear) with the kinetic energy conservation equation (quadratic). Rearranging and factoring both together yields (v₁ − v₂) = −(v₁' − v₂'): the relative velocity reverses sign but not magnitude. This is a powerful shortcut — it replaces the quadratic energy equation with a linear one, making 1D elastic collision problems much faster to solve than working with the full system of equations directly.
Question 4 True / False
In a 1D elastic collision, the heavier incoming object typically stops after impact, transferring most its kinetic energy to the lighter stationary object.
TTrue
FFalse
Answer: False
Complete velocity transfer (the incoming object stopping) only occurs when the two objects have equal mass. When the incoming object is heavier, it continues forward — barely slowing — while pushing the lighter object ahead at roughly twice its own speed. When the incoming object is lighter, it bounces back. Only the equal-mass case produces a full stop of the first object. The mass ratio determines what fraction of momentum and energy transfers, and only equal masses transfer everything.
Question 5 Short Answer
Why must both momentum conservation and kinetic energy conservation be applied simultaneously to solve an elastic collision? What goes wrong if only one law is used?
Think about your answer, then reveal below.
Model answer: Each conservation law alone gives one equation with two unknowns (the two final velocities), leaving the system underdetermined — infinitely many final velocity combinations satisfy either law alone. Momentum conservation is satisfied by any outcome that preserves total momentum, including objects passing through each other or sticking together. Kinetic energy conservation alone also allows multiple solutions. Only by applying both simultaneously do we get two independent equations for two unknowns, fully determining the final velocities from initial conditions.
This is the algebraic heart of elastic collision analysis. The uniqueness of the solution (given specific initial conditions) is what makes the elastic case so powerful: two constraints, two unknowns, fully determined. In inelastic collisions, kinetic energy is not conserved — some is lost to heat or deformation — so we need additional information (like 'objects stick together') to replace the energy constraint.