h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

As presented here there are some errors in how the laws are written.

Law Two states that a force, P (taking this from a mathematical perspective), is directly proportional to the RATE OF CHANGE OF MOMENTUM (not to the acceleration). It is a consequence of this that the formula can be rearranged to state F = ma but for some problems the original form (F = dp/dt) is more useful.

Law Three is more accurately written as: As Body A exerts a force, P, on Body B then Body B exerts an equal but opposite force on Body A. In the form given in the article then it is liable to misinterpretation to say that the forces act on the same body which they don't or nothing would ever move.

Joe aka Arnia

Pedantic mathematician fishies

Certainly you are correct on this point. F = ma is only true providing 'm' is constant. Since the original (and less popular) form of the equation states:

F {is proportional to} d(mv)/dt

this also allows for the rate of change of mass dm/dt.

This scenario is more common than most people think. Any vehicle that expells matter as part of its propulsion system (e.g a rocket, a motorcar) will get lighter whilst providing its motive force. Therefore, given a constant propulsion force, the acceleration of the vehicle will increase.

a = F/(m - Dm)

where Dm (for sake of argument) is the rate of mass of fuel loss.

As an interesting note, the modern Arian (spelling?) rockets that the european space agency are so fond of actually compensate for this.

During their flight path, the motive force is slowly reduced, keeping the acceleration constant. I'm not sure why they do this, but presumably it's for reasons of fuel efficiency. Maybe it also makes flight plans easier to programme.

There's another problem, referred to as the Newton-Murphy-Law:

1. Any object in motion will be heading in the wrong direction.
2. Any object at rest will be in the wrong place.

Did you know that Newton's Laws aren't Laws as such. What I mean is: they can't be proven. They are just generalisations made by experience. Very useful and correct most of the time, but someday, they might be considered not quite right, anymore (if that's not the case already, i.e. in thermodynamics).