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Re: [Phys-L] defining energy



I'd like to point out an interesting comparison of momentum and energy.

The momentum change of a system is dp = sum of (F_i*dt) = sum of (F_i)*dt =
F_net*dt. We can factor out the dt because all of the forces act for the
same time interval.

The energy change of a system is dE = sum of (F_i dot dr_i) if work is the
only input. We cannot in general factor out the dr_i because different
forces may act through different displacements, unless the system is a
point particle or all the forces act through the same displacement (e.g. a
rigid body that doesn't rotate). In these latter cases we can write dE =
sum of (F_i) dot dr = F_net dot dr.

This is perhaps related to the fact that there is only one kind of impulse
but many kinds of energy inputs, and only one kind of momentum but many
kinds of energy.

Bruce