A 40,000 kg railroad car initially traveling at 10 m/s collides inelastically 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 two cars after the inelastic collision, we can use the principle of conservation of momentum.
The conservation of momentum states that 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. It can be calculated using the formula:
Momentum (p) = mass (m) × velocity (v)
For the first railroad car:
Mass (m1) = 40,000 kg
Velocity (v1) = 10 m/s
For the second railroad car:
Mass (m2) = 20,000 kg
Velocity (v2) = 0 m/s (initially at rest)
Since the collision is inelastic, the two cars stick together, and they move as a single combined system after the collision.
Let's assume the final velocity, in meters per second, of the combined railroad cars is vf.
According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision:
(mass of first car × initial velocity of first car) + (mass of second car × initial velocity of second car) = (mass of combined car system × final velocity of combined car system)
Mathematically, it can be written as:
(m1 × v1) + (m2 × v2) = (m1 + m2) × vf
Substituting the given values into the equation:
(40,000 kg × 10 m/s) + (20,000 kg × 0 m/s) = (40,000 kg + 20,000 kg) × vf
(400,000 kg·m/s) + (0 kg·m/s) = (60,000 kg) × vf
400,000 kg·m/s = 60,000 kg × vf
Now, we can solve for the final velocity (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 inelastic collision is 6.67 m/s.