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Impulse and Collisions
Elastic vs Inelastic, Impulse-Momentum Theorem, and Coefficient of Restitution
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Impulse and collisions explain how forces change motion during short interactions like a bat hitting a ball or two carts bumping on a track. These ideas matter because they connect force, time, momentum, and energy in one event. By studying collisions, students can predict final speeds and understand why some impacts are bouncy while others involve sticking or deformation. The topic is central in mechanics, engineering, sports science, and vehicle safety.
Impulse is the product of force and the time interval over which it acts, and it equals the change in momentum of an object. In every isolated collision, total momentum is conserved, but kinetic energy is conserved only in elastic collisions. In an inelastic collision, some kinetic energy is transformed into sound, heat, or internal deformation. Comparing elastic and inelastic cases helps students separate what is always conserved from what depends on the type of interaction.
Key Facts
- Momentum is p = mv.
- Impulse is J = FΔt.
- Impulse equals change in momentum: J = Δp = mvf - mvi.
- Total momentum is conserved in an isolated system: Σpi = Σpf.
- Kinetic energy is KE = 1/2 mv^2.
- Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve momentum but not kinetic energy.
Vocabulary
- Momentum
- Momentum is the quantity of motion of an object, equal to its mass times its velocity.
- Impulse
- Impulse is the effect of a force acting over a time interval and equals the change in momentum.
- Elastic collision
- An elastic collision is a collision in which total momentum and total kinetic energy are both conserved.
- Inelastic collision
- An inelastic collision is a collision in which momentum is conserved but some kinetic energy is converted into other forms.
- Isolated system
- An isolated system is a system with no significant external force, so its total momentum stays constant.
Common Mistakes to Avoid
- Assuming kinetic energy is always conserved in every collision, which is wrong because only elastic collisions conserve total kinetic energy.
- Ignoring direction when using momentum, which is wrong because momentum is a vector and opposite velocities must have opposite signs.
- Using momentum conservation for one object instead of the whole system, which is wrong because momentum is conserved for the combined isolated system of all colliding objects.
- Confusing force with impulse, which is wrong because impulse depends on both the force and how long it acts, not just the force alone.
Practice Questions
- 1 A 0.50 kg ball moving at 8.0 m/s to the right is hit and leaves at 6.0 m/s to the left. What impulse acts on the ball?
- 2 A 2.0 kg cart moving at 4.0 m/s to the right collides and sticks to a 3.0 kg cart initially at rest. What is their final velocity?
- 3 Two collisions have the same total momentum before and after impact. One is elastic and one is inelastic. Explain how the kinetic energy behavior differs and what physical signs might show that energy changed form.