a 65.0 kg boy and his 40.0 kg sister, both wearing roller blades, face each othe

Question

a 65.0 kg boy and his 40.0 kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with velocity 2.90 m/s toward the west. Ignore friction. a) Describe the subsequent motion of the girl. b)How much potential energy in the girl's body is converted into mechanical energy of the boy-girl system? c) Is the momentum of the boy-girl system conserved in the pushing-apart process? If so, explain how that is possible considering d) there are large forces acting and e) there is no motion beforehand and plenty of motion afterward.

Explanation / Answer

a) Since linear momentum IS conserved, the momentum of the girl is actually -4.7125*40 = -188.5 kg m/s (opposite direction from the boy).
When this is added to the boy's momentum (+188.5), the result is zero.
This is expected since the initial momentum is also zero.

b) ME = KE = ½MV² = ½(65*2.9² + 40*4.7125²) = 717.48 J

c) as explained in a), The velocities (vectors) are opposite and the individual momenta therefore cancel leaving zero, the same as before the pushing.

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