AP Physics Questions on Perfectly Inelastic Collisions

📚 Quick Study Guide

🔍 Perfectly Inelastic Collisions: These collisions conserve momentum, but not kinetic energy. The objects stick together after the collision. 💡 Key Characteristics: * Kinetic energy is lost (usually converted to heat or sound). * Maximum kinetic energy loss occurs. * Objects move with a common final velocity. 📝 Conservation of Momentum: The total momentum before the collision equals the total momentum after the collision. Mathematically, this is expressed as: $m_1v_1 + m_2v_2 = (m_1 + m_2)v_f$ Where: * $m_1$ and $m_2$ are the masses of the two objects. * $v_1$ and $v_2$ are the initial velocities of the two objects. * $v_f$ is the final common velocity of the two objects after the collision. ⚛️ Kinetic Energy Loss: The change in kinetic energy ($\Delta KE$) is always negative in perfectly inelastic collisions, indicating a loss. It can be calculated as: $\Delta KE = KE_{final} - KE_{initial} = \frac{1}{2}(m_1 + m_2)v_f^2 - (\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2)$

🧪 Practice Quiz

1. A 2 kg mass moving at 3 m/s collides perfectly inelastically with a 1 kg mass at rest. 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. A car of mass 1000 kg moving at 20 m/s collides head-on with a stationary truck of mass 2000 kg. If they stick together after the collision, what is their common velocity?
   1. 5.0 m/s
   2. 6.7 m/s
   3. 10.0 m/s
   4. 13.3 m/s
3. In a perfectly inelastic collision, which of the following is always conserved?
   1. Kinetic Energy
   2. Potential Energy
   3. Momentum
   4. Velocity
4. Two objects with equal mass collide perfectly inelastically. One is moving at +v and the other at -v. What is the final velocity of the combined mass?
   1. +v
   2. -v
   3. 0
   4. 2v
5. A bullet of mass 0.01 kg is fired into a stationary wooden block of mass 1 kg and becomes embedded in it. If the block with the bullet moves at a velocity of 0.5 m/s after the impact, what was the initial velocity of the bullet?
   1. 10 m/s
   2. 25 m/s
   3. 50.5 m/s
   4. 100 m/s
6. What happens to the kinetic energy in a perfectly inelastic collision?
   1. It is conserved.
   2. It increases.
   3. It decreases.
   4. It remains constant.
7. A 5 kg object moving at 4 m/s collides perfectly inelastically with a 2 kg object moving in the same direction at 2 m/s. What is the final velocity of the combined mass?
   1. 1.14 m/s
   2. 2.29 m/s
   3. 3.43 m/s
   4. 4.57 m/s