Guide me through this plz.
A single 1,300 kg cargo train car is rolling along a train track at 2.0 m/s when 400 kg of coal is dropped vertically into it. What is its velocity right afterward? Assume a closed system.
(Points : 1)
1.5 m/s
2.0 m/s
6.5 m/s
0.0011 m/s
momentum before = momentum after
1300 * 2 + 400 * 0 = 1700 v
v = 1300 * 2 / 1700
v = 1.5 m/s
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To solve this problem, we can use the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant before and after an event or interaction.
In this situation, the cargo train car is the isolated system. Before the coal is dropped, the momentum of the system is the momentum of the train car, equal to the product of its mass (1,300 kg) and velocity (2.0 m/s). Let's calculate it:
Initial momentum = mass * velocity
Initial momentum = 1,300 kg * 2.0 m/s
Initial momentum = 2,600 N·s
After the coal is dropped vertically into the train car, we need to find the final velocity of the train car. To do this, we need to use the principle of conservation of momentum. We consider the system as closed, where the initial momentum is equal to the sum of the momentum before and after the event.
Final momentum = Initial momentum
The final momentum is equal to the sum of the momentum of the train car and the momentum of the dropped coal. After the coal is dropped, it gains momentum equal to the product of its mass (400 kg) and its velocity, which we need to find. Let's denote the final velocity of the train car as Vf and the final velocity of the coal as Vc. So the final momentum is:
Final momentum = (mass of train car * Vf) + (mass of coal * Vc)
Since the train car and the coal were initially at rest vertically, the velocity of the coal just before being dropped is zero (Vc = 0 m/s).
Final momentum = (mass of train car * Vf) + (mass of coal * 0 m/s)
Final momentum = (1,300 kg * Vf) + (400 kg * 0 m/s)
Final momentum = (1,300 kg * Vf)
Now we set the final momentum equal to the initial momentum:
(1,300 kg * Vf) = 2,600 N·s
We can solve this equation to find Vf, the final velocity of the train car:
Vf = 2,600 N·s / 1,300 kg
Vf = 2.0 m/s
Therefore, the velocity of the train car right afterward is 2.0 m/s.
So, the correct answer is 2.0 m/s.