To determine the common velocity of the balls after the collision, we can apply the principles of conservation of momentum and conservation of kinetic energy.
First, let's calculate the initial momentum of the system before the collision:
Initial momentum = (mass of ball 1 × velocity of ball 1) + (mass of ball 2 × velocity of ball 2)
Ball 1: mass = 200g = 0.2kg, velocity = 8m/s Ball 2: mass = 300g = 0.3kg, velocity = 4m/s
Initial momentum = (0.2kg × 8m/s) + (0.3kg × 4m/s) = 1.6kg·m/s + 1.2kg·m/s = 2.8kg·m/s
Since the balls stick together after the collision, their masses combine:
Combined mass = mass of ball 1 + mass of ball 2 = 0.2kg + 0.3kg = 0.5kg
Now, using the conservation of momentum, the final momentum of the system after the collision is equal to the initial momentum:
Final momentum = 2.8kg·m/s
Since the balls stick together, their combined velocity after the collision is the common velocity we're looking for. Let's denote it as V.
Final momentum = combined mass × common velocity
2.8kg·m/s = 0.5kg × V
Solving for V:
V = 2.8kg·m/s / 0.5kg = 5.6m/s
Therefore, the common velocity of the balls after the collision is 5.6 m/s.