Maximizing Runner's Acceleration: The Role of Friction

[furor celtica]

Homework Statement

Explain why a runner’s acceleration cannot exceed 10µ ms^-2, where µ is the coefficient of friction between her shoes and the track.

Homework Equations

The Attempt at a Solution

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?

 

[rl.bhat]

Just observe the process of walking or running.
She pushes the foot backward. The motion of the point of contact is therefore backward. Hence the frictional force on her is in the forward direction which enables her to move in the forward direction. The maximum frictional force is μ*m*g.

 

[furor celtica]

thanks