A boy of mass mb and his girlfriend of mass mg, bothwearing ice skates, face each other at rest while standing ona frictionless ice rink. The boy pushes the girl, giving her avelocity vg toward the east. Assume that mb > mg. (a) Describethe subsequent motion of the boy. (b) Find expressions forthe final kinetic energy of the girl and the final kinetic energyof the boy, and show that the girl has greater kinetic energy thanthe boy. (c) The boy and girl had zero kinetic energy before theboy pushed the girl, but ended up with kinetic energy after theevent. How do you account for the appearance of mechanicalenergy?

Question
Asked Dec 18, 2019
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A boy of mass mb and his girlfriend of mass mg, both
wearing ice skates, face each other at rest while standing on
a frictionless ice rink. The boy pushes the girl, giving her a
velocity vg toward the east. Assume that mb > mg. (a) Describe
the subsequent motion of the boy. (b) Find expressions for
the final kinetic energy of the girl and the final kinetic energy
of the boy, and show that the girl has greater kinetic energy than
the boy. (c) The boy and girl had zero kinetic energy before the
boy pushed the girl, but ended up with kinetic energy after the
event. How do you account for the appearance of mechanical
energy?

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Expert Answer

Step 1

Let the initial velocity of the boy be denoted as v1 and the initial velocity of the boy be denoted as v2

From the law of conservation of linear momentum,

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P, = P; P; = m,v, +m,V2 P; = m,v, +m,'g - (1) m,v¡ +m,v2 = m,V½ +M,vg ......

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Step 2

Since initially both the girl and the boy are at rest v1 and v2, both will equal to zero.

From the above given information equation (1) can be rewritten as,

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0 %3D т,у, + т,v, т,v, — - т,g 'g'g т. (2) —Vь т, б0

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Step 3

 

From equation (2), it can be seen that velocity of the boy will be in the direction opposite to that of the girl.

So the velocity vb of the boy wil...

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