The real Equation of Force is F = ma

Today's Physics is stating that the Equation of Force is F = dp/dt.

We will analyze the equation of motion of rockets to see that the real Equation of Force is F = ma.

A rocket has variable mass in its trajectory and it's important to see its motion equation.

Let m be its variable mass at any instant in its movement composed by the mass of the rocket plus the mass of its contained fuel.

I have made a search in the internet about rocket motion equations and all the sites agree in the equation:
F = m(dv/dt) = -u(dm/dt) where u is the speed of the fuel expelled relative to the rocket.

Some web sites:

http://classicalmechanics.net/RocketMotion.htm

http://www.braeunig.us/space/propuls.htm

They all agree that the force acting on the rocket is due to the expelled mass and is F = -u(dm/dt) and that the equation of motion is F = m(dv/dt) = ma.

I assume the equation have been completely verified experimentally with enough precision from a long time ago.

It is evident that it is used the equation:

F = ma

 for the force and not:

F = dp/dt

By definition p = mv and dp/dt = m(dv/dt) + v(dm/dt).

They derive the rocket's equation of motion based on the principle of conservation of momentum but considering the momentum of the rocket with the totallity of the fuel (the contained plus the expelled fuel) at any moment and stating dp/dt = 0. After that they derive the equation of motion of the rocket as: m(dv/dt) = -u(dm/dt) and specifically say that  the force on the rocket is:

F = m(dv/dt) = -u(dm/dt)

m(dv/dt) = ma then it is clear that what is finally applied to the rocket to determine its movement is the equation F = ma and not F = dp/dt.

This indicates that today's Physics is wrong stating the Equation of Force as F = dp/dt.

The right equation for force is F = ma even when mass varies.

Note that the natural derivation of the famous equation E = mc² by Relativity Theory has no sense since it is based in the wrong relation F = dp/dt.

Relativity Theory becomes a wrong theory since it is based on a wrong law.

By definition:

p = mv

With partial derivatives:

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

Now as:

F = m(dv/dt)

then the valid equation for momentum and force is

Then the principle of conservation of the momentum p = mv must determine that p = 0 when no forces are applied and when there's no variation on the considered mass.

It can be observed that this principle can be applied to the rocket as was applied in the cited cases giving the same result. Considering the mass m' of the composed body of the rocket and the total fuel (the contained plus the expelled fuel) which does not vary:

F = 0  and dm'/dt = 0

then the "thrust" equation can be derived:

m(dv/dt) = -u(dm/dt)

where m is the mass of the rocket with its contained fuel.

Finally:

F = ma = m(dv/dt) = -u(dm/dt)

F = -u(dm/dt) is the force exerted on the rocket.