Collisions are short interactions where objects exert large forces on each other for a brief time. In physics, the key question is what stays the same before and after the collision. Total momentum is conserved in an isolated system, which makes collisions useful for studying motion in carts, balls, vehicles, and particles.
The main difference between elastic and inelastic collisions is whether kinetic energy is also conserved.
Key Facts
- Momentum of one object is p = mv.
- Total momentum is conserved in an isolated collision: m1v1i + m2v2i = m1v1f + m2v2f.
- Kinetic energy is KE = 1/2 mv^2.
- Elastic collision: total momentum and total kinetic energy are conserved.
- Inelastic collision: total momentum is conserved but total kinetic energy is not conserved.
- Perfectly inelastic collision: objects stick together, so m1v1i + m2v2i = (m1 + m2)vf.
Vocabulary
- Momentum
- Momentum is the quantity of motion of an object, equal to its mass times its velocity.
- 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 total momentum is conserved but some kinetic energy changes into other forms.
- Perfectly inelastic collision
- A perfectly inelastic collision is a collision in which the objects stick together and move with one final velocity.
- Isolated system
- An isolated system is a group of objects with no net external force acting on it during the interaction.
Common Mistakes to Avoid
- Assuming kinetic energy is always conserved is wrong because only elastic collisions conserve total kinetic energy.
- Forgetting velocity signs is wrong because momentum is a vector, so motion in opposite directions must have opposite signs.
- Using conservation of momentum for one object alone is wrong because momentum conservation applies to the total system, not to each object separately.
- Thinking lost kinetic energy disappears is wrong because it is transformed into heat, sound, deformation, or internal energy.
Practice Questions
- 1 A 2.0 kg cart moving at 3.0 m/s collides elastically with a 1.0 kg cart initially at rest. If the 2.0 kg cart moves at 1.0 m/s after the collision, what is the final velocity of the 1.0 kg cart?
- 2 A 0.50 kg ball moving at 6.0 m/s collides with a 0.50 kg ball at rest. They stick together after the collision. What is their shared final velocity, and how much kinetic energy was lost?
- 3 Two collisions have the same initial masses and velocities. In one, the objects bounce apart, and in the other, they stick together. Explain which collision has more kinetic energy after the collision and why momentum can still be conserved in both.