I'm a bit confused here, so could anyone show me how to calculate the power N thats needed to accelerate a spaceship, that is moving with a non-relativistic speed v and has a mass m, with the acceleration of a.

I'm a bit confused here, so could anyone show me how to calculate the power N thats needed to accelerate a spaceship, that is moving with a non-relativistic speed v and has a mass m, with the acceleration of a.The force action on the space ship, F = ma. during one second, this force will act thru a distance v *1sec = v (Don't worry about fact velocity is not constant for this second as power is an instaneous concept. This is just easy to compute.) Work is force times distance and power is work done in one second. Thus Power required is mav.

This is the simple answer and correct if the exhaust gas is stationary, but generally it is not. A more accurate view would also consider the change in kinetic energy of the gas mass exhaused in one second. For this you would need to know the exhaust velocity relative to the rocket. That is one must consider the work done on the gas as well as the rocket (assuming it is powered by expelling gas). Note that initially this gas mass in the rocket has little KE, but later if the gas is also traveling forward, this KE is a decrease from what the mass had as fuel traveling with the rocket.

when you are not sure how to calculate something, look to the units. a watt (unit of power) is a N·m/s. so this tells you that power (in watts) is a force(N) times a velocity(m/s). so P=Fv. or P=mav.

always remember, units are your friends. I can't tell you how many physics test problems I just guessed on, but watched my units, and gotten right. in fact there was one time where I was the only one in the class to get the "challenge" problem right, and not because I knew how to do it, but because it followed my units. it actually impress the teacher because I did it a way he never thought of before.

I actually didn't have a problem with getting there using the formulas, but it was the fact that the power needed was depending on the speed.
Somehow it seemed weird to me.. Actually it still does.. I should probably just get some sleep..

edit: first of all, i had gotten the formula for power wrong. (I wrote P=At, not P=A/t)
And secondly, I got over the weirdness feeling, when I realized, that the kinetic energy formula K=mv²/2 has the speed squared, so that the energy needed to further accelerate the body should get bigger as the speed increases.

I actually didn't have a problem with getting there using the formulas, but it was the fact that the power needed was depending on the speed.
Somehow it seemed weird to me.. Actually it still does.. I should probably just get some sleep..

edit: first of all, i had gotten the formula for power wrong. (I wrote P=At, not P=A/t)
And secondly, I got over the weirdness feeling, when I realized, that the kinetic energy formula K=mv²/2 has the speed squared, so that the energy needed to further accelerate the body should get bigger as the speed increases.As I explained in second post, the correct solution is more complex than you seem to realize even now. Yes, the dominate reason (normally) that the power required depends upon speed of the rocket is that the fast rocket travels further in one second than the slow one and thus the force applied acts thru a longer distance during each second. But the mass of the rocket is changing and the total change in kinetic energy of the system in one second must be supplied by the chemical energy in the fuel burnt during that second.

The total energy change includes the change in the energy of the mass that was in the rocket (as fuel) at the start of the second and is exhaust gas at the end of the second. (Actually a limiting process calculation must be done but for practical purposes you can use one second, not one microsecond etc.) The power times one second causes a change in total kinetic energy, not just the change in the KE of the rocket.

Note that when the rocket is traveling faster that the exhaust is, the KE change of the exhaust mass is negative and this subtracts from the increase in rocket KE. That is, at least part if not all of, the reason why the rocket is more efficient the faster it goes (air resistance being absent, etc).

The low efficiency of the rocket motor is very evident during the first second after liftoff. The power delivered to the rocket is P = mav, but this is only a tiny fraction of the power of the rocket motor. Most of the rocket motor power is accelerating the exhaust, not the rocket. The only way to avoid much of this inefficiency is to confine the exhaust - I.e. launch the rocket inside a tube, like a rifle or mortar shell. This may not be pratical and would certainly require a reduced rate of fuel burning until the rocket exits the confining tube.

PS to Cato:
Your units analysis is always a good check, but may not get the correct answer exactly.

non-relativistic speed v :eek: WHAT?

:eek: WHAT?

rockets speed. marked in formulas as "v". the speed is small enough, not to consider the relativistic effects.

As I explained in second post, the correct solution is more complex than you seem to realize even now.

I am aware that the problem is more complex, but I was just trying to find a rough estimate of the power needed at some speeds and masses.

Your units analysis is always a good check, but may not get the correct answer exactly.
you don't have to tell me, I had quite a few problems (mostly in homework because I would make sure I knew the proper procedure for tests) wrong by using that method. I basically use them as a "I wonder if this would work" tool. if I am trying to find a way to solve something, I will look at what info I have, and how to get/cancel the units I need/don't need and then figure out if what I did was legal. pretty much anything using calculus can't be done by winging it with units.

you don't have to tell me, I had quite a few problems (mostly in homework because I would make sure I knew the proper procedure for tests) wrong by using that method. I basically use them as a "I wonder if this would work" tool. if I am trying to find a way to solve something, I will look at what info I have, and how to get/cancel the units I need/don't need and then figure out if what I did was legal. pretty much anything using calculus can't be done by winging it with units. You would not have liked to have me as your physics teacher.

When I designed college freshman physics test, most of the problems had exactly the correct information to plug into a formula that we had recently discussed in class, but that produced the wrong answer. Only the students who really understood, not the ones that used an approach similar to yours (see what infro you have and what formula it fits) were able to do my problems.

It was usually necessary to first use part of the information given in the problem to calculate something not given, using formulae from earlier chapters/ lessons, and also necessary to ignore some information that was given. (Real life is like that.) After calculating the "missing values" (numbers not given) then one used one or more of the formulae from the chapter we had just completed to get the correct answer.

I really enjoyed teaching people trying to learn, even the less bright ones, and was glad to see some "formula memorizers" drop my course. Speed was never a problem for my students. I would stay til they gave up or finished. To further discourage rote memory approach, my tests were often "open book, open notes." Physics is about understanding, not memory skills.

A physics professor I had was the polar opposite. Tests were more about speed of memory recall than physics. We could use a calculator, that’s it. If you got less than 85% on any test, you flunked the course unless you could get 85% or more on a different version of the test in less time allotted. The smart ones dropped the class after hearing the rules. Most of the rest of us flunked, including moi, and I later heard that he got some kind of demotion.

You would not have liked to have me as your physics teacher.

When I designed college freshman physics test, most of the problems had exactly the correct information to plug into a formula that we had recently discussed in class, but that produced the wrong answer. Only the students who really understood, not the ones that used an approach similar to yours (see what infro you have and what formula it fits) were able to do my problems.

It was usually necessary to first use part of the information given in the problem to calculate something not given, using formulae from earlier chapters/ lessons, and also necessary to ignore some information that was given. (Real life is like that.) After calculating the "missing values" (numbers not given) then one used one or more of the formulae from the chapter we had just completed to get the correct answer.

I really enjoyed teaching people trying to learn, even the less bright ones, and was glad to see some "formula memorizers" drop my course. Speed was never a problem for my students. I would stay til they gave up or finished. To further discourage rote memory approach, my tests were often "open book, open notes." Physics is about understanding, not memory skills.
yeah, thats pretty much what my teacher did, on the normal test problems that is. he gave us one plug and chug problem once and everyone was confused because we were used to having to work about 5 small problems before we had enough info to do the main problem. my teacher used to give open book (like 10 years before I had him) but people would put notes in their books, so he gave us formula sheets.

sorry I gave you the wrong impression, I never just throw stuff into a formula, like I said, I will work it, and "then figure out if what I did was legal." I am not a slacker when it comes to physics, I was competing with another guy for the top grade in the class, I don't know who won, it was probably him because I over studied for a test and f*cked up. if the teacher dropped that test, my average would have been like 103%, instead it was like a 97 =[. at the height of the competition, I was calling the teacher at home (he wanted us to, he was a nice guy (he got is "open door" policy from john wheeler, yep that john wheeler) to get the homework from the next section. I would work the ~15 he gave us for homework, the 10 or so he did in class, and about 10 I thought might be like something on the test. it made class boring though, because I was ahead of everyone.