Imparting Linear Momentum: Examining a Train Car Example

[thonwer]

This is not a problem, it is just a concept check :shy:

What does it mean that something does not impart linear momentum to the rest of the system?

For example grain leaking out a train car.

 

[HallsofIvy]

If, for example, the car is moving left to right and the grain is leaking out downward. "Linear Momentum" is "mass times velocity" and is a vector quantity. The grain's momentum is downward but the car cannot move upward or downward and so its linear momentum does not change. Technically that is because there is an "external force", gravity and the push of the rails ffon the car.

 

[thonwer]

So, for example, supposing there are no external forces on the x axis, no friction and no air drag, if I have a car with a certain mass and no holes, and grain falls in the car, it would take the car a time t to reach some point.

And, if now I have the same car but with a hole in it which let's the grain to leak out at a rate of
b kg/s , would it take the same time t, to reach the same point?

 

[Doc Al]

So, for example, supposing there are no external forces on the x axis, no friction and no air drag, if I have a car with a certain mass and no holes, and grain falls in the car, it would take the car a time t to reach some point.

And, if now I have the same car but with a hole in it which let's the grain to leak out at a rate of
b kg/s , would it take the same time t, to reach the same point?

Those situations are different. When the grain leaks from the car, the speed of the grain equals that of the car. Not so when grain falls into the car. (Presumably.)

Imagine you were ice skating on a frictionless pond while carrying a heavy ball. If you drop the ball, will your speed change? But what if you were skating along without the ball and someone dropped it into your hands as you skated by. See the difference?

 

[thonwer]

Those situations are different. When the grain leaks from the car, the speed of the grain equals that of the car. Not so when grain falls into the car. (Presumably.)

Imagine you were ice skating on a frictionless pond while carrying a heavy ball. If you drop the ball, will your speed change? But what if you were skating along without the ball and someone dropped it into your hands as you skated by. See the difference?

Yes I see it, and also I see that I may have explained myself badly. In the second case the grain also falls in the car and then it starts leaking out :shy:

 

[Doc Al]

Yes I see it, and also I see that I may have explained myself badly. In the second case the grain also falls in the car and then it starts leaking out :shy:

Do you understand why grain leaking out of a car does not change the momentum of the car? But grain falling into the car does?

 

[thonwer]

Do you understand why grain leaking out of a car does not change the momentum of the car? But grain falling into the car does?

Not really...
The grain leaking does not, because it goes vertically down and the momentum of the car is horizontal.

The grain falling into does, because it increases the mass after the "collision" so it slows down?

 

[olivermsun]

The grain leaking out doesn't go vertically down. It's going vertical down and also forward because it came out of a moving car.

 

[Nathanael]

The grain falling into does, because it increases the mass after the "collision" so it slows down?

If you were moving alongside the car at the same speed and dropped sand into the car, you could drop as much sand as you wish (increasing the mass as much as you wish) and it would not affect the speed of the car.

But when the sand being dropped into the car is moving slower than the car, it "takes" some of the car's momentum to be brought up to speed.
(The momentum gained by the sand is equal to the momentum lost by the car.)


You can look at it in terms of mass if you wish: You have an increased mass with the same amount of momentum...
But the important part isn't that the sand adds mass, it's that the sand doesn't add momentum
(When the sand falls out, the car-system loses mass but it also (proportionally) loses momentum, so the speed is unchanged.)

 

[thonwer]

(When the sand falls out, the car-system loses mass but it also (proportionally) loses momentum, so the speed is unchanged.)

But I thought that when the grain leaks out it doesn't change the momentum. I'm confused :S

 

[Nathanael]

But I thought that when the grain leaks out it doesn't change the momentum. I'm confused :S

It doesn't change the momentum of the car itself (ignoring the sand in the car) but if you're looking at the car and the sand IN the car as a single system (the "car-system" as I called it) then the momentum does change (but the speed does not)

So the CAR'S momentum does not change when sand leaks out.
(But the "car-system's" momentum does change because when the sand falls out it's no longer a part of the "car-system")
I am very sorry for making this confusing, I was only trying to show you it from the "mass of the car" point of view.
(Because you mentioned that the mass of the car had an effect.)
Hopefully this cleared things up? Sorry about that.EDIT:
I keep saying sand but of course I mean to say grain (not that it makes a difference)

 

[thonwer]

It doesn't change the momentum of the car itself (ignoring the sand in the car) but if you're looking at the car and the sand IN the car as a single system (the "car-system" as I called it) then the momentum does change (but the speed does not)

So the CAR'S momentum does not change when sand leaks out.
(But the "car-system's" momentum does change because when the sand falls out it's no longer a part of the "car-system")



I am very sorry for making this confusing, I was only trying to show you it from the "mass of the car" point of view.
(Because you mentioned that the mass of the car had an effect.)
Hopefully this cleared things up? Sorry about that.

Now I get it thank you so in both cases I described, the car-system would reach the point at the same time? In the first one the grain would slow the car, and in the second one too but the grain leaking out would not affect the new speed or am I wrong?

 

[Nathanael]

Now I get it thank you so in both cases I described, the car-system would reach the point at the same time? In the first one the grain would slow the car, and in the second one too but the grain leaking out would not affect the new speed or am I wrong?

Yes, that is correct (assuming situation two is completely identical with situation one except that grain is now leaking out)

 

[Doc Al]

Not really...
The grain leaking does not, because it goes vertically down and the momentum of the car is horizontal.

The grain falling into does, because it increases the mass after the "collision" so it slows down?

Think in terms of Newton's laws. For the momentum of the car to change, something must exert a horizontal force on it.

When the grain (speed = 0 with respect to the ground) falls into the moving car, the car must exert a force on the grain to carry it along. That means that the grain exerts a force on the car, changing its momentum.

But when the grain (already moving along with the car) falls out a hole in the car, no horizontal forces are involved, so the momentum of the car is unchanged.

 

[thonwer]

Yes, that is correct (assuming situation two is completely identical with situation one except that grain is now leaking out)

Yes that's the situation, thank you