Max Acceleration from Friction w/ Coeff 0.95: 9.3 m/s2

[tmobilerocks]

Homework Statement

What is the greatest acceleration that can be generated by a runner if the coefficient of static friction between shoes and road is 0.95?

Homework Equations

Fnet = ma
Force of static friction: u_sN
Weight= mg

The Attempt at a Solution

FBD: Positive x-axis is to the right. Positive y-axis is to the top. Normal force pointing up, equal in magnitude to weight pointing down. Friction must point in the positive x direction.

f = ma_x
a_x = u_sg
a_max = (0.95*9.81)
= 9.3 m/s²

I just have one question. Does the friction force point to the right, in the direction of the positive x axis? Thanks!

 

[BvU]

To answer your one question yourself you can imagine trying to accelerate on an (almost) friction-free surface, such as ice.

 

[tmobilerocks]

So the friction force would point to the right? Due to Fnet = ma, the acceleration and net force should be in the same direction. The only way this is possible is the friction force pointing to the right.

 

[BvU]

Yes, if the runner is trying to accelerate in the positive x direction (I didn't find that all too clearly in the story...). Runner pushes backward, exercises a force in the -x direction. No slipping means there must be a force in the +x direction to offset it: the friction force.

Compare with car braking: friction slows it down. Accelerating: friction allows it to accelerate.