Linear Momentum - Person on a Plank on a frictionless surface

[crafty2288]

Homework Statement

A plank of length 6m is lying on a smooth horizontal surface and has a mass of 100kg. A 50kg girl walks from one end of the plank to the other. In this experiment, how far will the plank shift and what direction? Why?

Homework Equations

v_g will mean girl's velocity relative to ice.
v_p will mean plank's velocity relative to ice.
M(girl)V(girl)[initial] + M(plank)V(plank)[initial] = M(girl)V(girl)[final] + M(plank)V(plank)[final]

The Attempt at a Solution

I feel like I need the girl's velocity or I can't do this. I understand how to solve it, but can anyone help me to understand how I do it without knowing the girl's velocity?

Initial momentum = 0 (because she's at rest).
Final momentum = 0 (because it has to equal initial momentum)

M(girl)V(girl)[initial] + M(plank)V(plank)[initial] = M(girl)V(girl)[final] + M(plank)V(plank)[final]
0 + 0 = (50)*V(girl)f + (100)*V(plank)fOr am I making this harder than it needs to be?

 

[AEM]

The essence of this problem is that since all forces involved are internal to the system, the center of mass of the system (plank plus girl) does not move even though the girl and the plank do move. The velocity of the girl or the plank is immaterial, {though as a practical matter, she should move slowly :) }

 

[crafty2288]

The essence of this problem is that since all forces involved are internal to the system, the center of mass of the system (plank plus girl) does not move even though the girl and the plank do move. The velocity of the girl or the plank is immaterial, {though as a practical matter, she should move slowly :) }

Sorry... I'm not sure where to go from here then... The Plank clearly will move, so how then do i calculate it?

 

[AEM]

Okay, draw a picture of the girl on the plank. Label the girl's center of mass. Label the plank's center of mass. Look up how to calculate the center of mass of the girl + plank. That point doesn't move. However, the girls and the plank DO move. They have to move so that in their final position their combined center of mass is in the same place. Stare at your drawing a little while, and the answer should hit you.

 

[crafty2288]

(Assuming that you are looking at the Plank from the side, and the girl starts at the left. Left being 0m, Right being 6m.)

So the center of mass before the move is at 2m...

And the center of mass after the move is at 4m...Does this mean that in relation to the surface... The plank has shifted 2m to the left?

 

[AEM]

(Assuming that you are looking at the Plank from the side, and the girl starts at the left. Left being 0m, Right being 6m.)

So the center of mass before the move is at 2m...

And the center of mass after the move is at 4m...


Does this mean that in relation to the surface... The plank has shifted 2m to the left?

That looks right to me.