A momentous question!

[chiddler]

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A rocket is propelled forward by emitting gas from behind.

This is one of the answers that is wrong: "Kinetic energy of gas expelled is equal to the kinetic energy of the rocket".

Is this wrong just because they didn't include the word magnitude so the v's will be opposite signs?

 

[milski]

There's nothing that says that the KE will be the same. Also, KE is always positive and a scalar, so you did not miss anything talking about signs or magnitudes.

What stays the same is the total momentum of the system. So if you take it to be 0 before the rocket's engine is ignited, you have MV+mv=0 or MV=-mv, where M and V are mass and velocity of the rocket and m and v for the gas expelled. Since the masses are not the same, even the velocities are not going to have the same magnitude. Which is a good thing, since you're not limiting the speed of your rocked by the speed at which the gasses leave.

 

[MedPR]

A rocket is propelled forward by emitting gas from behind.

This is one of the answers that is wrong: "Kinetic energy of gas expelled is equal to the kinetic energy of the rocket".

Is this wrong just because they didn't include the word magnitude so the v's will be opposite signs?

No, KE is a scalar.

I don't know why it's wrong though.

 

[milski]

No, KE is a scalar.

I don't know why it's wrong though.

KE(rocket)+KE(gasses)=Potential (chemical) energy lost

There is nothing that would imply that the energies are the same.

 

[chiddler]

edit: wait a minute. thinking

 

[milski]

Ah you're right. I just proved this to myself mathematically. Can you please explain why the kinetic energies are not the same?

I understand that the momentums must be equal and that the velocities are different as well.

Because it would be a huge coincidence. 😉

Both the gasses and the rocket get KE from converting chemical PE. Both have constantly changing masses and speeds of this masses, and none of these changes is one that would make them the same.

When you have the same energies, it's usually when you have one of them converted to the other. Or both energies are coming from something that would do the same amount of work. Or some other of dependencies which would lead to them being the same. Here, they're just energies, nothing binding them to be the same.

That's a bit convoluted, but it's a bit like proving a negative. 😉

 

[chiddler]

KE(rocket)+KE(gasses)=Potential (chemical) energy lost

There is nothing that would imply that the energies are the same.

before you wrote this I proved it to myself by using a simple example of a 10kg lady throwing a 5 kg rock forward at 10m/s. Their kinetic energies are very different.

But i'm having difficulty proving to myself why they are different. Why are they different?

EDIT: dammit you got my comment preedit. don't reply to this yet!

 

[milski]

Haha, ok. I'll go get a coffee. Let me know if you want help with it. 😉

 

[chiddler]

Haha, ok. I'll go get a coffee. Let me know if you want help with it. 😉

thank you for your help <3

I never explicitly read the following, but this is just what I figured from dimensional analysis:

Momentum = kg * m/s
Force = kg * m/s^2

So force describes change in momentum per second, right? If they are equal in changing their momentums, shouldn't the force be the...same...

wait.

the force may be the same but that doesn't mean work one is the same, right?

See this seems like cheating. X amount of gas kinetic energy can produce X + 100 of rocket kinetic energy. I don't understand the discrepancy.

 

[mcloaf]

So force describes change in momentum per second, right? If they are equal in changing their momentums, shouldn't the force be the...same...

wait.

the force may be the same but that doesn't mean work one is the same, right?

Well, change in momentum is impulse, J = delta (mv) = Force x time

So the force will only be equal if the time is equal.

 

[milski]

See this seems like cheating. X amount of gas kinetic energy can produce X + 100 of rocket kinetic energy. I don't understand the discrepancy.

You're looking at the final result. What happens is that when the fuel burns, it's chemical potential energy is converted to KE of the expanding gasses. Some of these gasses go straight out of the nozzle, some hit the chamber or transfer part of that KE to the rocket. One way or another, some of their KE gets transferred to the rocket. In an ideal world, that would be 100% but we're stuck with less.

So in your case, you started with 2*X+100 KE, x+100 got transferred to the rocked and the rest left with the gasses.

 

[chiddler]

You're looking at the final result. What happens is that when the fuel burns, it's chemical potential energy is converted to KE of the expanding gasses. Some of these gasses go straight out of the nozzle, some hit the chamber or transfer part of that KE to the rocket. One way or another, some of their KE gets transferred to the rocket. In an ideal world, that would be 100% but we're stuck with less.

So in your case, you started with 2*X+100 KE, x+100 got transferred to the rocked and the rest left with the gasses.

Ohhohohohoh!

i understand now. thank you again!

 

[milski]

Ohhohohohoh!

Marry Christmas! 😉

i understand now. thank you again!