Reassure Me: Linear Momentum Homework

[Litcyb]

Homework Statement

Im not sure if I did this problem correctly, can someone please reassure me?!

Homework Equations

Conservation of Linear momentum

pf=pi

m1v1=m2v2

The Attempt at a Solution

M(initial)=100,000 kg
M(final)= 100,000kg-15,000kg= 85,000kg

V(initial)=20.0m/s
V(final)=?

P(initial)=P(final)

m1v1=m2v2

(100,000)(20.0)=(85,000)(vf)

vf=23.53 m/s

did i do this correctly?

 

[rude man]

It would be nice if one could speed up a train that way!

Time for a couple of thought experiments:
1. what if all the dropped sand were to fall on a frictionless plane embedded between the ties?
2. if instead of a frictionless plane the sand were stopped from moving by the ties, would the train know the difference?

 

[SammyS]

Homework Statement

I'm not sure if I did this problem correctly, can someone please reassure me?!

Homework Equations

Conservation of Linear momentum

pf=pi

m1v1=m2v2

The Attempt at a Solution

M(initial)=100,000 kg
M(final)= 100,000kg-15,000kg= 85,000kg

V(initial)=20.0m/s
V(final)=?

P(initial)=P(final)

m1v1=m2v2

(100,000)(20.0)=(85,000)(vf)

vf=23.53 m/s

did i do this correctly?

See, it's not all that hard to include an image of the problem in your post so it's easy to read.Who made up that problem ?

 

[Litcyb]

It is an example question from old quizzes. why? the problem doesn't make sense? can someone help me?

so would it be (100,000)(20)= (85,000)(vf) +(15,000)(20)?
because the sand that is falling out, has the same speed of the cart throughout the 30 mins

 

[kickingpaper]

The 15000*20 term is unneeded since your accounting for the loss in mass in the 85000*vf term. The question makes sense to me btw. Your first answer is right and it's easy too check if you think about the conservation of momentum. For momentum to be conserved means that the momentum after some event is equal to the momentum before the event. If the train is losing mass it makes sense for the train to speed up to conserve momentum. Likewise if the train had gained mass, it would slow down.

 

[gneill]

A change in momentum requires external forces to act on the object in the direction of that change. What force acts on the train in the direction of its motion if sand simply falls out the bottom?

 

[rude man]

It is an example question from old quizzes. why? the problem doesn't make sense? can someone help me?

so would it be (100,000)(20)= (85,000)(vf) +(15,000)(20)?
because the sand that is falling out, has the same speed of the cart throughout the 30 mins

Much better!

 

[Litcyb]

@Rude man, I am confused. so in general, M(total) *V(initial)= M(train)*V(final train) + m(of sand)* velocity( throughout the 30 mins)
which gives me vf=20m/s. which is sort of weird, since is the same velocity we started with.

Is it okay to think of it this way; that in order to have conservation of momentum, we need to still consider the mass that has fall out of the cart. thus, is the reason why we added (15,000)*(20).

however, is what kickingpaper said still valid?

The 15000*20 term is unneeded since your accounting for the loss in mass in the 85000*vf term. The question makes sense to me btw. Your first answer is right and it's easy too check if you think about the conservation of momentum. For momentum to be conserved means that the momentum after some event is equal to the momentum before the event. If the train is losing mass it makes sense for the train to speed up to conserve momentum. Likewise if the train had gained mass, it would slow down.

can someone please clarify this?

 

[rude man]

@Rude man, I am confused. so in general, M(total) *V(initial)= M(train)*V(final train) + m(of sand)* velocity( throughout the 30 mins)
which gives me vf=20m/s. which is sort of weird, since is the same velocity we started with.

Is it okay to think of it this way; that in order to have conservation of momentum, we need to still consider the mass that has fall out of the cart. thus, is the reason why we added (15,000)*(20).

Yes. The sand has the same velocity and mass as before it was tossed, so there is no change in momentum of the system.

Note what gneill said: in order to change the momentum of a system you have to exert an external force F on it: ∫F dt = Δp or F = dp/dt where p = momentum.

however, is what kickingpaper said still valid?

No.

 

[Litcyb]

And since there are no external forces acting on it, then momentum is conserved. so, we have to finish with what we started.

if there was a external forces, such as in a rocket thrust problem, then we will have to involve impulse, in order to calculate the the Vf of the rocket, right?

 

[SammyS]

It seems that there are some crazy answers lurking about in this thread.


Let's look at this as two objects:

1. The 15,000 of sand that leaks out of the railroad car. Is momentum conserved for this sand?

2. The railroad car along with the sand that hasn't leaked out. Is momentum conserved for this 85,000 kg compound object?
​

 

[rude man]

And since there are no external forces acting on it, then momentum is conserved. so, we have to finish with what we started.

if there was a external forces, such as in a rocket thrust problem, then we will have to involve impulse, in order to calculate the the Vf of the rocket, right?

If the train car were a rocket there would be momentum associated with the expelled gases, depending of course on their mass and velocity. But the total momentum including the rocket "remains" and the expelled gases would still be conserved since the rocket is not an external force.

A corollary of this is that the center of mass of the rocket and all the expelled gases does not move!

EDIT: remember that this is conditional on no friction with the rails. If there were friction on the rails then momentum is still conserved but now you'd have to include the entire Earth in the picture!

 

[rude man]

It seems that there are some crazy answers lurking about in this thread.


Let's look at this as two objects:

1. The 15,000 of sand that leaks out of the railroad car. Is momentum conserved for this sand?

​

No. That momentum is transferred to the Earth eventually.​

 

[SammyS]

No. That momentum is transferred to the Earth eventually.

I meant that question for OP. I should have made that clear.Added in Edit:
The title of this thread includes momentum, but the problem statement doesn't . Why the big concern over conservation of momentum for this problem? (Rhetorical question)

 

[rude man]

I meant that question for OP. I should have made that clear.

Yeah, because I got the impression you were directing your remarks at more than one individual. My mistake ...

 

[MostlyHarmless]

I meant that question for OP. I should have made that clear.Added in Edit:
The title of this thread includes momentum, but the problem statement doesn't . Why the big concern over conservation of momentum for this problem? (Rhetorical question)

As it was a bonus question, my guess is the problem was intended send you down the wrong track.

Edit: No pun intended. :)

 

[Litcyb]

Well guys! thank you either way!

 

[rude man]

I meant that question for OP. I should have made that clear.


Added in Edit:
The title of this thread includes momentum, but the problem statement doesn't . Why the big concern over conservation of momentum for this problem? (Rhetorical question)

The rationale for the answer, which i think most of us know, is still arguable via momentum conservation. See my post #2.