# Newton's second law -- rockets

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• Woopa
In summary, the conversation discusses the concept of force and acceleration in relation to Newton's second law and the rocket equation. It is explained that in the case of an isolated system, the net force between the mass inside and any mass outside the system is zero, resulting in zero acceleration. However, the rocket and the propellant within the system still experience opposite accelerations. The conversation also highlights the misconception of using the change in velocity of the rocket and the velocity of the propellant in the equation for momentum conservation. In short, the conversation emphasizes the importance of considering the entire system and using the principle of momentum conservation in understanding the dynamics of the rocket.
Woopa
I am having difficulty understanding the information below. In the second line it states that F=0 as there is no external force on the system. However it later calculates acceleration of the rocket.

How can Force=0 if there is acceleration? (This is the first time I have encountered the product rule so this may be part of my misunderstanding)

The keyword here is "system". By considering both the propellant (initial at rest inside the rocket) and the rocket itself to be part of the system and then say this system is isolated we are effectively saying that the net force between the mass inside and any mass outside the system is zero, leaving us to consider only forces between mass inside the system. This then means the momentum of the system is unchanged, or equivalently, if one part of the system, e.g. some of the propellant, accelerate one way then another part, e.g. the rocket plus its remaining propellant, has to accelerate in the opposite direction.

topsquark, Ibix, PeroK and 1 other person
Woopa said:
Note that the "new form" of Newton's second law given here is not valid in general. There are several threads on here analysing this question.

In fact it's not really Newton's second law, but an equation that is only valid in this specific case.

PS the author has confusingly used the same letter ##v## for the velocity of the rocket and the velocity of the expellant. A simpler way to look at this is to use conservation of momentum:
$$m_r\Delta v_r + \Delta m_e v_e = 0$$Where we need the assumption that ##\Delta m_e## is small compared to ##m_r##. Otherwise, we would need to be more explicit that the mass of the rocket is changing from ##m_r + m_e## to ##m_r## after the expellent is fired out.

Last edited:
Filip Larsen, vanhees71 and topsquark
erobz, vanhees71, PeroK and 1 other person
PS if we are being harsh, then the author has made two mistakes which cancel out and contrive to get the right equation:

1) Wrongly stating Newton's second law as ##F = m\frac{\Delta v}{\Delta t} + v\frac{\Delta m}{\Delta t}##.

2) Mistakingly using the change in velocity of the rocket as ##\Delta v## and the velocity of the expellant as ##v## in this equation.

erobz, Ibix and vanhees71
Woopa said:
How can Force=0 if there is acceleration?
There is no acceleration. The rocket accelerates in one direction and the propellant accelerates in the opposite direction. The acceleration of the system (the system consisting of the rocket and the propellant) is zero.

## What is Newton's second law?

Newton's second law states that the force applied to an object is equal to its mass multiplied by its acceleration.

## How does Newton's second law apply to rockets?

In the case of rockets, the force is generated by the burning of fuel, which creates a thrust that propels the rocket forward. The mass of the rocket decreases as the fuel is burned, resulting in an increase in acceleration.

## What is the equation for Newton's second law?

The equation is F = ma, where F is the force, m is the mass of the object, and a is the acceleration.

## How does Newton's second law affect the design of rockets?

Newton's second law is a fundamental principle in rocket design. It is taken into account when determining the amount of fuel needed, the shape and size of the rocket, and the amount of thrust required for a successful launch.

## Are there any limitations to Newton's second law when it comes to rockets?

While Newton's second law is a crucial factor in rocket design, it does not take into account external forces such as air resistance and gravity. These forces can impact the acceleration and trajectory of the rocket and must be considered in the design process.

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