A sphere of mass 8 kg is moving at 3 m/s to the right until it smacks into a second stationary sphere of mass 2 kg. After the collision, both spheres travel to the right: the first sphere at 1.80 m/s, and the second sphere at 4.80 m/s. What kind of collision took place?
To determine what kind of collision took place, we need to analyze the conservation of momentum.
The initial momentum before the collision can be calculated by multiplying the mass (m1) and velocity (v1) of the first sphere:
Initial momentum before collision of the first sphere = m1 * v1 = 8 kg * 3 m/s = 24 kg·m/s
Since the second sphere is stationary, its initial momentum is zero:
Initial momentum before collision of the second sphere = m2 * v2 = 2 kg * 0 m/s = 0 kg·m/s
The total initial momentum before the collision is the sum of the individual momenta:
Total initial momentum = 24 kg·m/s + 0 kg·m/s = 24 kg·m/s
After the collision, the first sphere has a momentum of:
Momentum of the first sphere after collision = m1 * v1 = 8 kg * 1.80 m/s = 14.4 kg·m/s
The second sphere has a momentum of:
Momentum of the second sphere after collision = m2 * v2 = 2 kg * 4.80 m/s = 9.6 kg·m/s
The total final momentum after the collision is the sum of the individual momenta:
Total final momentum = 14.4 kg·m/s + 9.6 kg·m/s = 24 kg·m/s
Since the total initial momentum is equal to the total final momentum, this implies that momentum is conserved.
However, the velocities of the spheres before and after the collision are not the same. This means that kinetic energy is not conserved, indicating an inelastic collision.
In conclusion, an inelastic collision took place between the spheres.