- #1

brochesspro

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- TL;DR Summary
- My question inquires about the meaning of each of the terms present in the formula for the net external force on a system and uses rocket propulsion as an example to further clarify the concept.

The mathematical representation of the net external force on a system(obtained from Newton's second law) is ##\vec F_{net} = \frac {d\vec P}{dt}##, which is the rate of change of linear momentum of the system. If we substitute ##\vec P = m\vec v## into the formula for force and differentiate, we get:$$\vec F_{net} = m\frac{d\vec v}{dt} + \frac {dm}{dt}\vec v.$$

What do the terms ##m##, ##\frac{d\vec v}{dt}##, ##\frac {dm}{dt}##, ##\vec v## mean exactly? Could you use rocket propulsion as an example to explain the meaning of these terms? I have an idea of what each of these could be in this case, please check whether they are right or wrong. Here, the system I am choosing is the total mass of the rocket and the ejected gas and the term "rocket" refers to the rocket and the gas present in the rocket.

##m## is the total mass of the rocket at any given instant.

##\frac{d\vec v}{dt}## is the rocket's acceleration at a given instant in time.

##\frac {dm}{dt}## is the rate at which the gas is ejected out of the rocket to propel it.

##\vec v## is the rocket's velocity at any given instant(I am especially not sure of this one, but the same goes for the others.).

Thank you for answering.

What do the terms ##m##, ##\frac{d\vec v}{dt}##, ##\frac {dm}{dt}##, ##\vec v## mean exactly? Could you use rocket propulsion as an example to explain the meaning of these terms? I have an idea of what each of these could be in this case, please check whether they are right or wrong. Here, the system I am choosing is the total mass of the rocket and the ejected gas and the term "rocket" refers to the rocket and the gas present in the rocket.

##m## is the total mass of the rocket at any given instant.

##\frac{d\vec v}{dt}## is the rocket's acceleration at a given instant in time.

##\frac {dm}{dt}## is the rate at which the gas is ejected out of the rocket to propel it.

##\vec v## is the rocket's velocity at any given instant(I am especially not sure of this one, but the same goes for the others.).

Thank you for answering.

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