Macroscopic Collisions Quiz: Test Your Physics Knowledge

📚 Quick Study Guide

• ⚖️ Momentum Conservation: In a closed system, the total momentum before a collision equals the total momentum after the collision. Mathematically, $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$, where $m$ is mass, $v$ is velocity, $i$ denotes initial, and $f$ denotes final.
• 💥 Types of Collisions:
  • 🧊 Elastic Collisions: Kinetic energy is conserved.
  • 🔥 Inelastic Collisions: Kinetic energy is not conserved (some energy is lost as heat or sound).
  • 🧱 Perfectly Inelastic Collisions: Objects stick together after the collision.
• 💡 Kinetic Energy: The energy of motion, given by $KE = \frac{1}{2}mv^2$.
• 📐 Coefficient of Restitution (e): A measure of the elasticity of a collision. $e = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}}$. $e = 1$ for elastic collisions, and $e = 0$ for perfectly inelastic collisions.
• ✍️ Impulse: The change in momentum of an object. $J = \Delta p = F\Delta t$, where $J$ is impulse, $F$ is the force, and $\Delta t$ is the time interval.

🤔 Practice Quiz

1. A 2 kg ball moving at 3 m/s collides head-on with a 1 kg ball at rest. If the collision is perfectly inelastic, what is the final velocity of the combined mass?
   1. 1 m/s
   2. 2 m/s
   3. 3 m/s
   4. 4 m/s
2. In an elastic collision, which of the following is conserved?
   1. Only momentum
   2. Only kinetic energy
   3. Both momentum and kinetic energy
   4. Neither momentum nor kinetic energy
3. A 5 kg object moving at 4 m/s hits a wall and bounces back at 2 m/s. What is the magnitude of the impulse experienced by the object?
   1. 10 Ns
   2. 20 Ns
   3. 30 Ns
   4. 40 Ns
4. Two cars collide at an intersection. Car A (1000 kg) is moving east at 20 m/s and Car B (1500 kg) is moving north at 10 m/s. If they stick together after the collision, what is the approximate magnitude of their velocity immediately after the collision?
   1. 8.0 m/s
   2. 10.0 m/s
   3. 12.0 m/s
   4. 14.0 m/s
5. What is the coefficient of restitution for a perfectly elastic collision?
   1. 0
   2. 0.5
   3. 1
   4. 2
6. A bullet of mass 0.01 kg is fired into a wooden block of mass 1 kg resting on a horizontal surface. The bullet gets embedded in the block, and the block moves a distance of 0.2 m before coming to rest. If the coefficient of friction between the block and the surface is 0.5, what was the initial velocity of the bullet?
   1. 100 m/s
   2. 141 m/s
   3. 200 m/s
   4. 241 m/s
7. Which of the following is true for a perfectly inelastic collision?
   1. The objects bounce off each other with equal and opposite velocities.
   2. The objects stick together after the collision.
   3. Kinetic energy is conserved.
   4. Momentum is not conserved.