Momentum Conservation in Closed Systems: Worked Example Problems

📚 Momentum Conservation in Closed Systems: Quick Study Guide

• ⚖️ Law of Conservation of Momentum: In a closed system (no external forces), the total momentum remains constant.
• 📝 Momentum Formula: Momentum ($p$) is the product of mass ($m$) and velocity ($v$): $p = mv$.
• 🎯 Total Momentum: The total momentum of a system is the vector sum of the momenta of all its objects.
• 💥 Collisions: In collisions, momentum is conserved. We have elastic (kinetic energy conserved) and inelastic (kinetic energy not conserved) collisions.
• 🚀 Formula for Conservation of Momentum: $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$, where $i$ denotes initial and $f$ denotes final.
• 💡 Closed System: A system where no external forces act upon it.

🧪 Practice Quiz

1. What is the primary condition for momentum to be conserved in a system?
   1. A) External forces are present.
   2. B) No external forces are present.
   3. C) Kinetic energy is conserved.
   4. D) Potential energy is conserved.
2. Two objects collide inelastically. Which of the following is conserved?
   1. A) Kinetic energy
   2. B) Momentum
   3. C) Both kinetic energy and momentum
   4. D) Neither kinetic energy nor momentum
3. A 2 kg ball is moving at 3 m/s. What is its momentum?
   1. A) 5 kg m/s
   2. B) 6 kg m/s
   3. C) 7 kg m/s
   4. D) 8 kg m/s
4. Two carts, one with mass 1 kg and moving at 2 m/s, and another with mass 2 kg and at rest, collide and stick together. What is their final velocity?
   1. A) 2/3 m/s
   2. B) 3/2 m/s
   3. C) 1 m/s
   4. D) 0 m/s
5. Which of the following is an example of a nearly closed system where momentum conservation can be effectively applied?
   1. A) A car accelerating on a road.
   2. B) A ball falling with air resistance.
   3. C) Two billiard balls colliding on a table.
   4. D) A rocket launching into space.
6. A 5 kg object moving at 4 m/s collides with a stationary 1 kg object. If they stick together, what is their combined final speed?
   1. A) 10/3 m/s
   2. B) 20/3 m/s
   3. C) 5 m/s
   4. D) 1 m/s
7. What distinguishes an elastic collision from an inelastic collision?
   1. A) Only momentum is conserved in elastic collisions.
   2. B) Only kinetic energy is conserved in elastic collisions.
   3. C) Both momentum and kinetic energy are conserved in elastic collisions.
   4. D) Elastic collisions only occur in outer space.