Question

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A 50.0-kg boy and his 39.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.40 m/s toward the west. Ignore friction. (a) Describe the subsequent motion of the girl. She will move east, directly away from her brother with a speed 4.36 m/s. She will move east, directly away from her brother with a speed 1.7 m/s. She will move east, directly away from her brother with a speed 6.06 m/s. She will move west, in the same direction as her brother, with a speed 3.40 m/s. (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? Yes NO (d) If so, explain how that is possible considering there are large forces acting. (If momentum is not conserved, enter "Momentum is not conserved.") This answer has not been graded yet. (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.") This answer has not been graded yet.

Answer 1

solution : PART: A P = Initial momentin of girl-boy system = (50 xo + 39x0) = 0 - 0 P = Final momentim of girl-boy system. - PE = moyo+ Mg Vg PF = 50x (-3.4 m/s) + 3 gxva s ☺ If we consider girl and boy as one system the force appli ed by girl is internal force, therefore No external force is there. from Newton's second Law Vg - 39 Part B JZ P = conet. = Peis Pg from o and o= -50x3.47 39 Vq Vg = 5x3o4 mes. = 4.36 m/s. opposite S to boy direction Mechanical Energy of system eintially=P-E-7K-E. Total Mechanical Energy of system after push- - 2 m ve 2 mg Vg² - 2x50x (-3-4)2 + 4x 39X (4:36) ? = 289 +370.68 = 1659.68 Joule Therefore same energy must be reduced from girls Internal potential Energy Part :c If we consider girl and boy as one system the force applied by girl is internal force, therefore No external force is there a from Newton 11nd Law Force = dp = 0 dz B = const. or conserved. Parto & According to Newton's second Law momentem will change only where there is net resultant external force on systerno The push applied by girl is internal force which can not change momentim of the system