Question

# A 53.0-kg boy and his 37.0-kg sister, both wearing roller blades, face each other at rest....

A 53.0-kg boy and his 37.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 2.70 m/s toward the west. Ignore friction.

(a) Describe the subsequent motion of the girl.

She will move west, in the same direction as her brother, with a speed 2.70 m/s.She will move east, directly away from her brother with a speed 3.87 m/s.    She will move east, directly away from her brother with a speed 1.35 m/s.She will move east, directly away from her brother with a speed 5.22 m/s.

(b) How much potential energy in the girl's body is converted into mechanical energy of the boy–girl system?
J

(c) Is the momentum of the boy–girl system conserved in the pushing-apart process?

YesNo

(d) If so, explain how that is possible considering there are large forces acting. (If momentum is not conserved, enter "Momentum is not conserved.")

(e) 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.")

Given that

The mass of the boy mb =53kg

The mass of the girl is mg =37kg

Final velocity of the boy is vfb =-2.70m/s

a)

Now from the law of conservation of momentum

mbvib+mgvig=mbvfb+mgvfg

0 =53kg*(-2.70)+37(vfg)

Now vfg is given by =143.1/37=3.867m/s

Therefore the speed of the girl is vgf =3.867m/s

b)

Now the potential energy in the girls body is the total kineitc energy of boy and girl

KE of the gril =(1/2)mgvg2 =0.5*37(3,867)2 =276.72J

KE of the boy =(1/2)mbvb2 =0.5*53(-2.70)2 =193.185J

Total KE =469.905J Which is nearly equal to =470J

c)

Here the momentum remains conserved because the according to the law of conservation of momentum when there is no external force acting on the system, the momntum remains conserved.

d)

If the external force acts on the system the momentum does not remains conserved

e)

if we consider the there is no motion beforehand and plenty of motion afterward also the momentum is not conserved.