A group of 4 rail cars with a total mass of 50,000kg moves at 3m/s at a stationary locomotives that has a mass of 10,000kg. What is the speed of the whole train after the cars connect with the locomotive?
F=ma
50,000kg*3m/s= 150,000kg m/s
150,000kg m/s divided by 60,000kg
a= 2.5m/s
a is usually used for acceleration, which is m/s^2.
You ought to have used v, which in fact was entirely omitted:
50000*3 = 60000v
v = 2.5 m/s
Your answer was correct, but the "a" was misleading.
To calculate the speed of the whole train after the cars connect with the locomotive, we can use the equation F=ma, where F is the net force applied on the system, m is the total mass of the system, and a is the acceleration.
Initially, the rail cars have a total mass of 50,000 kg and they are moving at a speed of 3 m/s. Therefore, the momentum of the rail cars is given by the product of their mass and velocity, which is equal to 50,000 kg * 3 m/s = 150,000 kg·m/s.
The locomotive has a mass of 10,000 kg and is stationary, meaning it has zero momentum.
When the rail cars connect with the locomotive, the two objects become one system. The sum of their momenta before the connection should be equal to the sum of their momenta after the connection, due to the law of conservation of momentum.
Since the momentum of the locomotive is initially zero, the total momentum of the system after the connection is equal to the momentum of the rail cars.
Now, we need to find the speed of the whole train after the connection. This can be done by dividing the total momentum by the total mass of the system.
In this case, the total mass of the system is the sum of the mass of the rail cars (50,000 kg) and the mass of the locomotive (10,000 kg), which gives us a total mass of 60,000 kg.
Therefore, the acceleration (a) of the train after the cars connect with the locomotive is given by:
a = total momentum / total mass
a = (150,000 kg·m/s) / (60,000 kg)
a = 2.5 m/s
So, the speed of the whole train after the cars connect with the locomotive is 2.5 m/s.