Two identical gliders slide toward each other on an airtrack. One moves at 1 m/s and the other at 2 m/s. They collide and stick. The combined mass moves at ____ m/s.
Answer
To find the speed at which the combined mass moves, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. In this case, the total momentum before the collision is the sum of the momentum of the two gliders. Since the gliders are identical, they have the same mass.
Let's denote the mass of each glider as m and their initial velocities as v1 and v2. According to the problem, v1 = 1 m/s and v2 = 2 m/s.
The momentum of the first glider is given by:
momentum1 = mass * velocity1 = m * v1
Similarly, the momentum of the second glider is:
momentum2 = mass * velocity2 = m * v2
Before the collision, the total momentum is the sum of these two momenta:
total momentum before collision = momentum1 + momentum2
= m * v1 + m * v2
= m * (v1 + v2)
After the collision, the gliders collide and stick together, forming a combined mass. Let's denote the final velocity of the combined mass as v'.
The total momentum after the collision is given by:
total momentum after collision = combined mass * final velocity
= (2m) * v'
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
m * (v1 + v2) = (2m) * v'
Simplifying the equation:
v1 + v2 = 2v'
Substituting v1 = 1 m/s and v2 = 2 m/s:
1 + 2 = 2v'
3 = 2v'
Solving for v':
v' = 3/2 m/s
Therefore, the combined mass moves at a speed of 3/2 m/s after the collision.