Final answer:
To find the coefficient of restitution, we calculate the final velocity of the masses after the collision. The coefficient of restitution is determined by the relative velocity of separation and the relative velocity of approach. In this case, the masses travel together after the collision, resulting in a coefficient of restitution of 0.
Step-by-step explanation:
To find the coefficient of restitution, we need to apply the conservation of momentum principle. The equation for the conservation of momentum in an elastic collision is:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where m₁ and m₂ are the masses of the two objects, u₁ and u₂ are their initial velocities, and v₁ and v₂ are their final velocities after the collision.
In the given problem, the mass m₁ is moving with velocity 5 m/s and the mass m₂ is stationary. After the collision, both masses travel together with the same velocity. Since there is no information about the velocities after the collision, we can assign them as v.
Using the equation for the conservation of momentum, we get:
100 kg * 5 m/s + 1000 kg * 0 m/s = (100 kg + 1000 kg) * v
Simplifying the equation, we find that v = 0.5 m/s.
The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In this case, since the masses travel together after the collision, the relative velocity of separation is 0 m/s. Therefore, the coefficient of restitution is 0.