# Acceleration, friction

1. Sep 27, 2010

### furor celtica

1. The problem statement, all variables and given/known data
Explain why a runner’s acceleration cannot exceed 10µ ms^-2, where µ is the coefficient of friction between her shoes and the track.
2. Relevant equations

3. 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?

2. Sep 27, 2010

### 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.

3. Sep 27, 2010

thanks