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Conservation of Momentum
Elastic and Inelastic Collisions, Explosions, and Center of Mass
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Momentum is a measure of how hard it is to stop a moving object, and it depends on both mass and velocity. The conservation of momentum is one of the most important ideas in physics because it lets us predict what happens in collisions, explosions, and recoils. In an isolated system with no net external force, the total momentum stays constant. This principle is used in fields ranging from sports science to rocket motion.
Momentum is a vector quantity, so both size and direction matter when adding it for a system. During a collision, individual objects may speed up, slow down, or reverse direction, but the total momentum of all interacting objects remains the same if external forces are negligible. This works for elastic collisions, inelastic collisions, and explosions. The key is to define the system carefully and account for signs when objects move in opposite directions.
Key Facts
- Momentum of one object: p = mv
- SI unit of momentum: kg·m/s
- Conservation law: Σp_before = Σp_after
- For two objects in one dimension: m1v1i + m2v2i = m1v1f + m2v2f
- If an object is initially at rest, then its initial momentum is p = 0
- Momentum is conserved only when the net external force on the system is zero or negligible
Vocabulary
- momentum
- Momentum is the product of an object's mass and velocity, showing how much motion it has.
- isolated system
- An isolated system is a group of objects with no significant external forces acting on it.
- collision
- A collision is an interaction in which objects exert forces on each other for a short time.
- elastic collision
- An elastic collision is a collision in which both momentum and kinetic energy are conserved.
- inelastic collision
- An inelastic collision is a collision in which momentum is conserved but kinetic energy is not.
Common Mistakes to Avoid
- Ignoring direction, which is wrong because momentum is a vector and opposite directions must be given opposite signs.
- Using conservation of momentum for a single object, which is wrong because the law applies to the total momentum of a system of interacting objects.
- Assuming kinetic energy is always conserved, which is wrong because only elastic collisions conserve both momentum and kinetic energy.
- Forgetting external forces, which is wrong because momentum is conserved only if the net external force on the system is zero or small enough to ignore.
Practice Questions
- 1 A 2.0 kg cart moves to the right at 3.0 m/s and collides with a 1.0 kg cart at rest. After the collision, the 2.0 kg cart moves at 1.0 m/s to the right. What is the final velocity of the 1.0 kg cart?
- 2 A 0.50 kg ball moving at 8.0 m/s to the left hits a wall and rebounds at 6.0 m/s to the right. What is the change in momentum of the ball?
- 3 Two skaters push off from each other on nearly frictionless ice. Explain why they move in opposite directions and how their momenta compare.