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Posted: Mar 18 2010, 07:37 PM
Joined: 18-March 10
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How is it that most textbooks state Newton II as F=dp/dt where p=mv and that this reduces to F=ma for constant mass particle. Surely it is the other way round? F=ma and this reduces to F=dp/dt for constant mass.
Obviously both statements are the same for constant mass particle. But what about variable mass particles.
I understand that most variable mass particles (rockets raindrops etc) are, in reality, systems of particles that are loosing particles, and so are not really particles.
Suppose you had an atom moving at constant velocity and acted on by no force. It's nucleus spontneousl moves to a higher energy level converting some of the atom's mass into internal energy. So its a system of particles that has not lost any particles , but whose mass has changed.
Then if F=0=dp/dt then p = mv is constant and since m decreased v must increase. so a decrease in mass gives a increase in velocity?
If F=0=ma=mdv/dt then v remains constant. Surely this is the real situation.
I suppose you could argue that conversion of mass into energy is a relativistic concept and does not apply in the Newtonian description. Plus you could say that the atom is a system and not a particle. But why don't we simply tell students that F=ma and that F=dp/dt only in the case of constant mass.