A 40,000 kg railroad car initially traveling at 10 m/s collides in elastically with a 20,000 kg railroad car intially at rest. The cars stick together. What is their final speed?
To find the final speed of the combined railroad cars after the collision, we can use the principle of conservation of momentum.
The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. Momentum is defined as the product of an object's mass and velocity.
In this case, we have two railroad cars colliding in an elastic collision. Since this is an elastic collision, the total kinetic energy before and after the collision should be conserved.
First, let's define the variables:
m1 = mass of the first car = 40,000 kg
v1 = initial velocity of the first car = 10 m/s
m2 = mass of the second car = 20,000 kg
v2 = initial velocity of the second car = 0 m/s (at rest)
The total momentum of the system before the collision can be calculated as:
initial momentum = (m1 * v1) + (m2 * v2)
Since the second car is initially at rest, the equation becomes:
initial momentum = (m1 * v1) + (m2 * 0)
Now, let's calculate the initial momentum:
initial momentum = (40,000 kg * 10 m/s) + (20,000 kg * 0) = 400,000 kg·m/s
According to the conservation of momentum principle, the total momentum before the collision should be equal to the total momentum after the collision.
Let's assume the final velocity of the combined cars is vf. In this case, the total momentum after the collision can be calculated as:
final momentum = (m1 + m2) * vf
Equating the initial momentum to the final momentum:
400,000 kg·m/s = (40,000 kg + 20,000 kg) * vf
Simplifying the equation:
400,000 kg·m/s = 60,000 kg * vf
Now, let's solve for vf:
vf = 400,000 kg·m/s / 60,000 kg
vf ≈ 6.67 m/s
Therefore, the final velocity of the combined railroad cars after the collision is approximately 6.67 m/s.