How to interper thrust of the rocket

[amiras]

For example then talking about the rocket the trust is:

F_thrust = u*dm/dt

where u is speed of the gases relative to the rocket, and dm/dt rate of change of ejected mass of gases.

Now if the rocket is being launched vertically so force of gravity acts upon it and:

F_net = F_thrust - mg = u*dm/dt - mg

According to the 2nd Newton's law:

F_net = dp/dt = v*dm/dt + m*dv/dt = v*dm/dt + ma

If comparing these equations:

ma=-mg in this case:

should that be interpreted that the acceleration a is caused by the forces other then thrust.

And is it possible to write:

F_net = m*dv/dt + F_other = F_thrust + F_other

 

[bp_psy]

For example then talking about the rocket the trust is:

F_thrust = u*dm/dt

where u is speed of the gases relative to the rocket, and dm/dt rate of change of ejected mass of gases.

Now if the rocket is being launched vertically so force of gravity acts upon it and:

F_net = F_thrust - mg = u*dm/dt - mg

According to the 2nd Newton's law:

F_net = dp/dt = v*dm/dt + m*dv/dt = v*dm/dt + ma

If comparing these equations:

ma=-mg in this case:

should that be interpreted that the acceleration a is caused by the forces other then thrust.

And is it possible to write:

F_net = m*dv/dt + F_other = F_thrust + F_other

u*dm/dt =/= v*dm/dt
Since u is the speed of the ejected gas with respect to the rocket and v is the velocity of the rocket with respect to some fixed frame.This is clearly ma=-mg wrong.
The acceleration of the rocket depends on both the weight of the rocket and the thrust. The higher the weight the smaller the acceleration for some given thrust.

 

[K^2]

amiras, you are forgetting that the rocket is also losing amount of momentum proportional to lost mass. So dp/dt = F_net + v*dm/dt, so you get F_net = m dv/dt = ma. (This is one of the subtler parts of deriving rocket formula.)

So: ma = u dm/dt - mg.

 

[Delta Kilo]

First, as bp_psy said, u /= v

F_net = dp/dt = v*dm/dt + m*dv/dt

While this looks like a mathematically correct way to differentiate a product of two functions of t, you have to be carefult about physical significance of that.

The second term m*dv/dt is the force required to accelerate mass m from v to v+dv during time dt. This is ok. But the first term v*dm/dt means the force required to accelerate a small mass increment dm from 0 to v during time dt (or decelerate it from v to 0, depending on the sign of dm). In other words this equation quietly assumes that the extra mass acquired (or lost) by the moving body has initial (or final) velocity of 0.

The reason why it doesn't quite work is because mass (unlike other parameters, like velocity or temperature) does not just appear out of nowhere, it actually moves from one part of the system to another and carries its momentum with it. For that reason it is easier to treat the mass as a constant during differentiation and then explicitly account for the momentum brought in (or carried away) by the mass flow.

It's a subtle point, see here for some examples and discussion:
http://books.google.com.au/books?id=Ni6CD7K2X4MC&pg=PA690

PS the correct expression in your case if F_net = ma = u dm/dt - mg
PPS just noticed K^2 said the same thing already

 

[pmacias]

First, it is important to clarify that the thrust of a rocket is the force that propels it forward. This is different from the acceleration of the rocket, which is the rate of change of its velocity.

To interpret the thrust of a rocket, we can use the equation F_thrust = u*dm/dt, where u is the speed of the gases relative to the rocket and dm/dt is the rate of change of the ejected mass of gases. This equation tells us that the thrust of the rocket is directly proportional to the speed of the ejected gases and the rate at which they are ejected.

In the example of a vertically launched rocket, we also need to take into account the force of gravity acting on the rocket. This can be represented by the equation F_net = F_thrust - mg, where m is the mass of the rocket and g is the gravitational acceleration. This equation shows that the net force acting on the rocket is the difference between the thrust and the force of gravity.

Applying the second law of motion, F_net = dp/dt = m*dv/dt + ma, we can see that the acceleration of the rocket is caused by both the change in its mass (due to the ejection of gases) and the net force acting on it. So, in this case, the acceleration is caused by both the thrust and the force of gravity.

It is not accurate to say that the acceleration is caused by forces other than thrust, as the thrust itself is a force that contributes to the acceleration. However, we can say that the net force acting on the rocket, which includes both thrust and other forces such as gravity, is what ultimately determines the acceleration of the rocket.

To summarize, the thrust of a rocket is the force that propels it forward and is directly related to the speed and rate of ejection of gases. The acceleration of the rocket is determined by the net force acting on it, which includes both the thrust and other forces such as gravity. It is not accurate to say that the acceleration is caused by forces other than thrust, as thrust itself is a contributing force to the acceleration.