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 railroad cars after colliding, you can apply the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) can be calculated as:
p = mass × velocity
Therefore, the momentum of the first railroad car before the collision is given by:
p1 = mass1 × velocity1
Similarly, the momentum of the second railroad car before the collision is:
p2 = mass2 × velocity2
Since the second car is initially at rest (velocity2 = 0), its momentum is zero.
To find the total momentum before the collision (p_total), we add the individual momenta:
p_total = p1 + p2
After the collision, the two cars stick together, meaning they move as one combined system. Let's denote the final velocity of the two cars, which stick together, as "v_final."
To find the total momentum after the collision, we multiply the combined mass of the cars by the final velocity:
p_total = (mass1 + mass2) × v_final
According to the law of conservation of momentum, p_total (before the collision) should be equal to p_total (after the collision). Therefore, we can set these two equations equal to each other:
p1 + p2 = (mass1 + mass2) × v_final
Now let's plug in the given values:
mass1 = 40,000 kg (mass of the first car)
velocity1 = 10 m/s (initial velocity of the first car)
mass2 = 20,000 kg (mass of the second car, initially at rest)
velocity2 = 0 m/s (initial velocity of the second car)
p1 = 40,000 kg × 10 m/s
p2 = 20,000 kg × 0 m/s
Simplifying the equation, we get:
40,000 kg × 10 m/s + 20,000 kg × 0 m/s = (40,000 kg + 20,000 kg) × v_final
400,000 kg·m/s = 60,000 kg × v_final
Dividing both sides by 60,000 kg, we can find the final velocity:
v_final = 400,000 kg·m/s ÷ 60,000 kg
Simplifying, we get:
v_final = 6.67 m/s
Therefore, the final velocity of the two railroad cars after colliding and sticking together is 6.67 m/s.