Solved Examples: Conservation of Linear Momentum in Closed Systems

📚 Quick Study Guide

• 🍎 Definition: Conservation of linear momentum states that the total momentum of a closed system remains constant if no external forces act on it.
• 📏 Closed System: A closed system is one where no mass enters or leaves, and no external forces are present.
• ➕ Total Momentum: The total momentum of a system is the vector sum of the momenta of all the objects in the system.
• ➗ Formula: If you have two objects (1 and 2) colliding:
  • 📝 Momentum before collision = Momentum after collision
  • $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$
  • Where:
    • $m_1$ and $m_2$ are the masses of the objects.
    • $v_{1i}$ and $v_{2i}$ are the initial velocities of the objects.
    • $v_{1f}$ and $v_{2f}$ are the final velocities of the objects.
• 💡 Key Idea: Momentum is a vector quantity, meaning direction matters!

Practice Quiz

1. A 2 kg ball is moving at 3 m/s to the right. It collides head-on with a 1 kg ball moving at 4 m/s to the left. If the 2 kg ball is moving at 1 m/s to the right after the collision, what is the velocity of the 1 kg ball?

   1. -2 m/s
   2. 2 m/s
   3. -6 m/s
   4. 6 m/s

2. A 5 kg bowling ball is rolling at 2 m/s when it strikes a stationary 0.5 kg pin. If the bowling ball slows to 1.5 m/s after the collision, how fast is the pin moving?

   1. 4 m/s
   2. 5 m/s
   3. 0.5 m/s
   4. 2.5 m/s

3. A 1500 kg car is at rest. A 50 kg person jumps out of the car with a horizontal velocity of 1 m/s. What is the change in velocity of the car?

   1. 0.033 m/s
   2. -0.033 m/s
   3. 30 m/s
   4. -30 m/s

4. Two ice skaters, with masses of 50 kg and 70 kg, are standing stationary in the middle of a rink. They push off each other. If the 50 kg skater moves with a velocity of 2 m/s, what is the recoil velocity of the 70 kg skater?

   1. 2 m/s
   2. -2 m/s
   3. 1.43 m/s
   4. -1.43 m/s

5. A rocket expels 100 kg of exhaust gas at a velocity of 2000 m/s. If the rocket's mass is 1000 kg, what is the change in the rocket's velocity?

   1. 100 m/s
   2. 200 m/s
   3. 2000 m/s
   4. 20 m/s

6. A 0.2 kg hockey puck is sliding on ice at 5 m/s when it collides with a stationary 0.1 kg puck. If the 0.2 kg puck slows to 3 m/s after the collision, what is the velocity of the 0.1 kg puck?

   1. 2 m/s
   2. 4 m/s
   3. 6 m/s
   4. 8 m/s

7. A bullet of mass 0.01 kg is fired from a gun of mass 5 kg. If the bullet leaves the gun with a velocity of 300 m/s, what is the recoil velocity of the gun?

   1. 0.6 m/s
   2. -0.6 m/s
   3. 1.5 m/s
   4. -1.5 m/s