
friction, acceleration
Explain why a runner’s acceleration cannot exceed 10µ ms^2, where µ is the coefficient of friction between her shoes and the track.
Ok here I have a big problem, I have no idea which formula to use to model this type of motion or resolve these forces. I think they want me to deduce it or something, I would be tempted to use a=F/m=10mµ/m where F=10mµ, i.e. the model for a frictional force, with g=10 for normal reaction 10m and µ coefficient of friction. But this doesn’t take into account any of the forces exerted by the runner except for her weight, which looks like a clumsy model to me…
Any hints?

Based on the wording of this problem, you're going to have to make an assumption or two. One is the highly problematic value of g = 10 m/s^2. (9.8 is much closer to the actual value). The other is that the mu given is the coefficient of static friction.
So, if you think about the runner pushing backwards against the track, how would you draw a freebody diagram? How is friction modeled?