A girl of mass m G is standing on a plank of mass m P . Both are originally at r

Question

A girl of mass mG is standing on a plank of mass mP. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vGP to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.)

(a) What is the velocity vPI of the plank relative to the surface of the ice? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

(b) What is the girl's velocity vGI relative to the ice surface? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

Explanation / Answer

The total momentum remains zero and the center of mass remains in the original location.

(a) The plank's velocity (relative to ice) is vpi. The girl's velocity relative to ice is vgp + vpi

Mp*vpi + Mg(vgp + vpi) = 0
vpi (Mg + Mp) = -Mg*vgp
vpi = -[Mg/(Mg+Mp)]*vgp

Let mG/mP = R

vpi = -vgp*R/[1 + R]

(b) vgi = vgp + vpi
= vgp{1 - [Mg/(Mg+Mp)]}
= vgp*[Mp/(Mg +Mp)] (1/(R+1) = mp/(mg +mp) )

vgi = -vpi/R

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