A railroad car of mass 2500 kg moving at 5.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 2.20 m/s. (a) What is the speed of the three coupled cars after the collision?
momentum before= momentum after
m*5+2*m*2.2=3mV
solve for V
To solve this problem, we can use 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.
First, let's calculate the momentum of each car before the collision:
Momentum of the single car = mass of single car * velocity of single car
Momentum of the single car = 2500 kg * 5.00 m/s = 12500 kg·m/s
Momentum of the two coupled cars = (mass of each coupled car * velocity of each coupled car) + (mass of each coupled car * velocity of each coupled car)
Momentum of the two coupled cars = (2500 kg * 2.20 m/s) + (2500 kg * 2.20 m/s) = 5500 kg·m/s + 5500 kg·m/s = 11000 kg·m/s
The total momentum before the collision is the sum of the momentum of the single car and the momentum of the two coupled cars:
Total momentum before the collision = Momentum of the single car + Momentum of the two coupled cars
Total momentum before the collision = 12500 kg·m/s + 11000 kg·m/s = 23500 kg·m/s
After the collision, the three cars will be coupled and moving together at a common speed. Let's call this final speed "v".
Now, let's calculate the momentum of the three coupled cars after the collision:
Momentum of the three coupled cars = (total mass of the three cars) * v
Momentum of the three coupled cars = (2500 kg + 2500 kg + 2500 kg) * v = 7500 kg * v
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before the collision = Total momentum after the collision
23500 kg·m/s = 7500 kg * v
Now we can solve for v:
v = (23500 kg·m/s) / (7500 kg) = 3.13 m/s
Therefore, the speed of the three coupled cars after the collision is 3.13 m/s.