mu′ − mu = ξ.
(37)
The effect of ordinary finite forces during the infinitely short duration of this impulse is of course ignored.
We may apply this to the theory of impact. If two masses m1, m2 moving in the same straight line impinge, with the result that the velocities are changed from u1, u2, to u1′, u2′, then, since the impulses on the two bodies must be equal and opposite, the total momentum is unchanged, i.e.
m1u1′ + m2u2′ = m1u1 + m2u2.
(38)
The complete determination of the result of a collision under given circumstances is not a matter of abstract dynamics alone, but requires some auxiliary assumption. If we assume that there is no loss of apparent kinetic energy we have also
m1u1′2 + m2u2′2 = m1u12 + m2u22.
(39)
Hence, and from (38),