Using the expressions for the
velocities
of masses m1
and m2,
we may determine the total kinetic energy
Ekin,total
of the system of the two masses.
Ekin,total =
½ m1 v12
+ ½ m2 v22
Ekin,total =
½ ( m1 + m2
) VCM2
+ ½ μ v 2
We find one term which expresses the kinetic energy of an object
of mass m1 + m2,
representing the total mass of the system of two masses,
and which travels with the center-of-mass velocity
VCM(t)
and one term which represents the internal kinetic energy of an object
of reduced mass μ, defined by
μ = m1m2
/ (m1 + m2)
and with velocity equal to the relative velocity
v of mass m2
with respect to mass m1.
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