In a completely elastic collisions a ball with speed of 4 m/s and mass of 100 g hits another ball with mass of 200 g, which is originally at rest. Collision is central. Calculate the velocity of both balls just after the collision.
To calculate the velocity of both balls just after the collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In a completely elastic collision, kinetic energy is also conserved.
First, let's calculate the initial momentum of the system:
Initial momentum = (mass of ball 1 * velocity of ball 1) + (mass of ball 2 * velocity of ball 2)
Since the second ball is originally at rest, its initial velocity is 0 m/s:
Initial momentum = (100 g * 4 m/s) + (200 g * 0 m/s)
Next, let's calculate the mass-weighted final velocity of the system. Since the collision is central, we assume that both balls share the same final velocity (v):
Final momentum = (mass of ball 1 * velocity) + (mass of ball 2 * velocity)
Using the principle of conservation of momentum, we equate the final momentum with the initial momentum:
Initial momentum = Final momentum
(100 g * 4 m/s) + (200 g * 0 m/s) = (100 g + 200 g) * velocity
Simplifying,
(100 g * 4 m/s) = (300 g) * velocity
400 g m/s = 300 g * velocity
Dividing both sides by the mass of the balls,
velocity = (400 g m/s) / (300 g)
velocity ≈ 1.33 m/s
Therefore, the velocity of both balls just after the collision is approximately 1.33 m/s.