A 70.0-kg boy and his 44.0-kg sister, both wearing roller blades, face each othe

Question

A 70.0-kg boy and his 44.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.80 m/s toward the west. Ignore friction. Describe the subsequent motion of the girl. How much potential energy in the girl's body is converted into mechanical energy of the boy-girl system? Is the momentum of the boy-girl system conserved in the pushing-apart process? If so, explain how that is possible considering there are large forces acting. (If momentum is not conserved, enter "Momentum is not conserved.") If so, explain how that is possible considering there is no motion beforehand and plenty of motion afterward. (If momentum is not conserved, enter "Momentum is not conserved.")

Explanation / Answer

a)

linear momentum consevation

mass of boy * boy velocity = mass of girl * girl velocity

70*3.8 =44*v

v =6.05 m/s in east

b)

mechanical energy boy-girl system =kinetic energy of boy + kinetic energy of girl

                                                   = 1/2 *70*(3.8)2 + 1/2*44*(6.05)2 =505.4 + 805.255 =1310.655 J

c)

yes

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