Understanding the Concepts
* Momentum: A measure of an object's mass in motion. It's calculated as momentum (p) = mass (m) * velocity (v).
* Conservation of Momentum: In a closed system (no external forces), the total momentum before a collision equals the total momentum after the collision.
* Perfectly Inelastic Collision: A collision where the objects stick together after impact, resulting in a single combined mass.
The Problem
You're given:
* m1: Mass of object 1
* m2: Mass of object 2
* v1: Initial velocity of object 1
* v2: Initial velocity of object 2
The Goal
You want to find the final velocity (v) of the combined mass after the collision.
Solution
1. Calculate the initial momentum:
* Momentum of object 1: p1 = m1 * v1
* Momentum of object 2: p2 = m2 * v2
* Total initial momentum: p_initial = p1 + p2
2. Calculate the final momentum:
* Combined mass: M = m1 + m2
* Final velocity (unknown): v
* Total final momentum: p_final = M * v
3. Apply conservation of momentum:
* p_initial = p_final
* (m1 * v1) + (m2 * v2) = (m1 + m2) * v
4. Solve for the final velocity (v):
* v = (m1 * v1 + m2 * v2) / (m1 + m2)
Important Note: This solution assumes the collision happens in a straight line. If the objects are moving at angles to each other, you'll need to use vector addition for momentum.
Example
Let's say:
* m1 = 2 kg
* m2 = 3 kg
* v1 = 4 m/s
* v2 = -2 m/s (moving in the opposite direction)
Then, the final velocity would be:
* v = (2 kg * 4 m/s + 3 kg * -2 m/s) / (2 kg + 3 kg) = 2/5 m/s
This means the combined mass will move at 2/5 m/s in the direction of the initial velocity of the heavier object (m2).
