# Momentum: I have the answer, now an explanation?

• TG3
In summary, the railroad hopper car has a mass of 40,000 kg when empty and 50,000 kg when filled with coal. As it travels at a constant speed of 4 m/s, it releases all of its coal over a period of 4 seconds. Using the equation for momentum, the car's final speed can be calculated to be 9 m/s. However, since there is no opposing force mentioned, the car will continue to move at a constant speed of 4 m/s. This is because the coal, even as it is dropped from the car, maintains its momentum and does not leave it behind. Therefore, the correct answer is 4 m/s, not 9 m/s.
TG3
So, I know the "correct" answer to this problem, but it makes no sense to me at all. Why is the following the case?

## Homework Statement

A railroad hopper car has mass 40,000 kg when empty and contains 50,000 kg of coal. As it coasts along the track at 4 m/s the hopper opens and steadily releases all the coal onto a platform below the rails over a period of 4 s.

How fast does the car travel after all the coal is dumped?

## Homework Equations

Momentum = Mass x Velocity

## The Attempt at a Solution

40,000+ 50,000 = 90,000
90,000 x 4 = 360,000

360,000 / 40,000 = 9 m/s.
This seems simple and obvious, yet the computer insists that the correct answer is 4 m/s. Why would this ever be...?

No friction or other force in the horizontal direction has been mentioned, so the car will continue in motion at its constant speed of 4 m/s. F = ma, F is zero so "a" is zero.

Why do you think it is the right answer?

Are you saying that as soon as each lump of coal was dropped from the car it left its momentum in the car?

!
I obviously wasn't considering that the coal continues moving as it is dropped, and doesn't leave it's momentum behind, which is the premise I was operating under. Many thanks!

## 1. What is momentum?

Momentum is a physics concept that refers to the quantity of motion in an object. It is a measure of how much an object's mass and velocity contribute to its overall motion.

## 2. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = m * v, where p is momentum, m is mass, and v is velocity.

## 3. What is the unit of measurement for momentum?

The unit of measurement for momentum is kilogram-meter per second (kg*m/s). This is because momentum takes into account both mass (measured in kilograms) and velocity (measured in meters per second).

## 4. What is the principle of conservation of momentum?

The principle of conservation of momentum states that the total momentum of a closed system (a system with no external forces acting on it) remains constant. This means that momentum can be transferred between objects within the system, but the total momentum will always remain the same.

## 5. How does momentum impact collisions?

In a collision, the total momentum of the objects involved is conserved. This means that the sum of the momentums before the collision will be equal to the sum of the momentums after the collision. This principle is used in fields such as car safety, where engineers design cars to absorb and distribute momentum in a collision to minimize the force on the passengers.

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