Conservation of Momentum: A Car Crash Scenario?

📌 CONCEPT: The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision. This principle applies to all types of collisions, whether elastic or inelastic. In an inelastic collision, the objects stick together after the impact.

📐 RULE / FORMULA: The rule for conservation of momentum is given by the equation: m1u1 + m2u2 = (m1 + m2)v, where m1 and m2 are the masses of the objects, u1 and u2 are their initial velocities, and v is the final velocity of the combined objects.

💡 WORKED EXAMPLE: A 1000 kg car is traveling at 30 m/s and collides with a 2000 kg truck traveling at 5 m/s. After the impact, the vehicles come to rest. Using the law of conservation of momentum, we can calculate the final velocity of the combined wreckage. Applying the formula, 1000 kg × 30 m/s + 2000 kg × 5 m/s = (1000 kg + 2000 kg) × v. Solving for v, we get v = -0.125 m/s. The negative sign indicates that the combined wreckage is moving in the opposite direction of the initial velocities.

⚠️ COMMON MISTAKE: Students often forget to consider the direction of the velocities when applying the law of conservation of momentum. It is essential to take into account the direction of the velocities to ensure accurate calculations.