A 15000 kg railroad car moving 7m/s to the North collides with and sticks to another railroad car of the same mass that is moving the same direction at 1.5 m/s. What type of collision is this? What is the velocity of the joined cars after the collision?
it is an inelastic collision, solve by setting initial momentum equal to final momentum.
To determine the type of collision, we need to consider whether there is any external force acting on the system of two railroad cars. In this case, since there is no mention of an external force, we can assume that the collision is an isolated system with no external forces.
In an isolated system, the law of conservation of momentum applies. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the momentum of the first car can be calculated as:
Momentum of first car = mass of first car × velocity of first car
= 15000 kg × 7 m/s
= 105,000 kg·m/s (north direction)
Similarly, the momentum of the second car can be calculated as:
Momentum of second car = mass of second car × velocity of second car
= 15000 kg × 1.5 m/s
= 22,500 kg·m/s (north direction)
Total momentum before the collision = Momentum of first car + Momentum of second car
= 105,000 kg·m/s + 22,500 kg·m/s
= 127,500 kg·m/s (north direction)
Since the two cars stick together after the collision, they can be considered as one combined mass. Let's call the velocity of the joined cars after the collision as v.
The total momentum after the collision can be calculated as:
Total momentum after the collision = (Mass of first car + Mass of second car) × Velocity of joined cars
= (15000 kg + 15000 kg) × v
= 30000 kg × v
Since the total momentum before the collision is equal to the total momentum after the collision, we can set up an equation:
Total momentum before = Total momentum after
127,500 kg·m/s = 30000 kg × v
Now we can solve for v:
v = 127,500 kg·m/s / 30000 kg
v = 4.25 m/s
Therefore, the velocity of the joined cars after the collision is 4.25 m/s to the north.
As for the type of collision, since both cars stick together and move together after the collision, this is an example of an inelastic collision.