Q: Estimate the magnitude of the contact forces that the girls exert on one other.

Answer:

When applying Newton’s Laws (F_net=ma), we have to decide what is going to be our body (m). Only then would  we know which forces to include (those that act on m) and which forces to exclude (those that do not act on m).

If we analyse all four girls as one combined body, then our free body diagram looks like this.

This allows us to quickly confirm that the magnitude of the normal contact force that the floor exerts on each girl is mg.

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We can also analyse each girl as an individual body. Which leads us to following free body diagram.

Notice that F_u (upward contact force exerted by the next girl’s legs on this girl’s head) and F_d (downward contact force exerted by the previous girl’s head on this girl’s legs) did not feature in the earlier free body diagram. Why? Because as one combined body, these are internal forces.

Now, by considering the net moment about this girl’s foot (where N acts), we can estimate F_u to be about 0.5mg. Next, by considering the net force acting on this girl, F_d should also be about 0.5mg.

P.S. Yes, some assumptions have been made to simplify the analysis. I assumed that the girls have identical masses and dimensions. I also assumed that the C.G. is right at the middle. I also assumed F_u, F_d and N to be equidistant from the C.G.

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