Understanding the Concepts
* Momentum: Momentum is the measure of mass in motion. It's calculated as mass (m) times velocity (v): p = mv.
* Conservation of Momentum: In a closed system (like our colliding balls), the total momentum before a collision is equal to the total momentum after the collision.
Calculations
1. Calculate the initial momentum of each ball:
* Ball 1 (500 grams): p1 = (0.5 kg) * (4 m/s) = 2 kg m/s
* Ball 2 (200 grams): p2 = (0.2 kg) * (8 m/s) = 1.6 kg m/s
2. Calculate the total initial momentum:
* Total initial momentum (p_initial) = p1 + p2 = 2 kg m/s + 1.6 kg m/s = 3.6 kg m/s
3. Calculate the combined mass of the system:
* Total mass (m_total) = 0.5 kg + 0.2 kg = 0.7 kg
4. Apply the conservation of momentum to find the final velocity:
* Total initial momentum (p_initial) = Total final momentum (p_final)
* p_final = m_total * v_final
* v_final = p_final / m_total = 3.6 kg m/s / 0.7 kg = 5.14 m/s (approximately)
Answer
The velocity of the system (the two balls stuck together) after the collision is approximately 5.14 m/s.
