# Variable mass and rockets

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username2436711

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When solving variable mass problems with rockets ejecting fuel/ gas, can I calculate the thrust by considering the force exerted on the exhaust since it is equal and opposite?

i.e. dp/dt=(m)dv/dt + (v)dm/dt

where dm/dt = mass of exhaust ejected at speed v (cancelling first term since speed of ejection constant) ?

many thanks, sorry I don't have my specific example atm

i.e. dp/dt=(m)dv/dt + (v)dm/dt

where dm/dt = mass of exhaust ejected at speed v (cancelling first term since speed of ejection constant) ?

many thanks, sorry I don't have my specific example atm

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Eimmanuel

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#2

(Original post by

When solving variable mass problems with rockets ejecting fuel/ gas, can I calculate the thrust by considering the force exerted on the exhaust since it is equal and opposite?

i.e. dp/dt=(m)dv/dt + (v)dm/dt

where dm/dt = mass of exhaust ejected at speed v (cancelling first term since speed of ejection constant) ?

many thanks, sorry I don't have my specific example atm

**marinacalder**)When solving variable mass problems with rockets ejecting fuel/ gas, can I calculate the thrust by considering the force exerted on the exhaust since it is equal and opposite?

i.e. dp/dt=(m)dv/dt + (v)dm/dt

where dm/dt = mass of exhaust ejected at speed v (cancelling first term since speed of ejection constant) ?

many thanks, sorry I don't have my specific example atm

I hope the physics would be so simple. Unfortunately, it is NOT.

The thrust can be calculated as

where

*v*

_{gas}is the velocity of the exhaust gas

*dm*relative to the rocket

*m*.

dp/dt= (m)dv/dt + (v)dm/dt

This is abused of calculus.

The

*v*in (m)d

*v*/d

*t*and (

*v*)d

*m*/d

*t*is actually “different”. The d

*v*/d

*t*should be the acceleration of the rocket + exhaust gas while the

*v*is the relative velocity of the exhaust.

You can look at the actual derivation in this Wikipedia.

https://en.wikipedia.org/wiki/Variable-mass_system

You can try solving the following

Spoiler:

Ans : (a) 3.90 × 10

Show

Ans : (a) 3.90 × 10

^{7}N (b) 3.20 m/s

^{2}

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Forest 4ever

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steve44

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username2436711

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(Original post by

I hope the physics would be so simple. Unfortunately, it is NOT.

The thrust can be calculated as

where

dp/dt= (m)dv/dt + (v)dm/dt

This is abused of calculus.

The

You can look at the actual derivation in this Wikipedia.

https://en.wikipedia.org/wiki/Variable-mass_system

You can try solving the following

**Eimmanuel**)I hope the physics would be so simple. Unfortunately, it is NOT.

The thrust can be calculated as

where

*v*_{gas}is the velocity of the exhaust gas*dm*relative to the rocket*m*.dp/dt= (m)dv/dt + (v)dm/dt

This is abused of calculus.

The

*v*in (m)d*v*/d*t*and (*v*)d*m*/d*t*is actually “different”. The d*v*/d*t*should be the acceleration of the rocket + exhaust gas while the*v*is the relative velocity of the exhaust.You can look at the actual derivation in this Wikipedia.

https://en.wikipedia.org/wiki/Variable-mass_system

You can try solving the following

Spoiler:

Ans : (a) 3.90 × 10

Show

Ans : (a) 3.90 × 10

^{7}N (b) 3.20 m/s

^{2}

^{Thanks for clearing that up }

^{When you say it’s abused of calculus, do you mean I’ve differentiated wrong? Or that the terms just have the different meanings? Like I used implicit/chain rules, but was that expression wrong? }

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Eimmanuel

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#6

(Original post by

Thanks for clearing that up When you say it’s abused of calculus, do you mean ….….

**marinacalder**)Thanks for clearing that up When you say it’s abused of calculus, do you mean ….….

I mean that you are NOT supposed to use product rule from calculus.

A lot of physics teachers or tutors had applied product rule to differentiate the product of mass and velocity, thinking that it is ok but it is wrong.

https://www.youtube.com/watch?v=oGe_dvjz9kg

https://www.youtube.com/watch?v=BB_B7Vkj2XY&t=151s

The result does not give the correct answer for all the situation in variable mass problems.

If you go to the Wikipedia link, you would see there was a paper that wrote about the “

__On the use and abuse of Newton's second law for variable mass problems__”

You don't need to read the whole paper, just the first two pages and it will reveal why it is wrong.

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