How do i find the coefficient of static friction?

[sam kim]

Homework Statement

A coffee cup in your dashboard slides forward when you decelerate from 20 m/s to rest in 3.5 s or less, but now if you decelerate for a longer time. What is the coefficient of static friction between your coffee cup and your dashboard?

Homework Equations

a = delta a / delta t, Ff = uFn (i think)

The Attempt at a Solution

I found out the maximum deceleration needed so that the cup doesn't move (a is < or = to -5.71) but i don't know how to find the coefficient of static friction

 

[Merlin3189]

A coffee cup in your dashboard slides forward when you decelerate from 20 m/s to rest in 3.5 s or less, but not if you decelerate for a longer time. What is the coefficient of static friction between your coffee cup and your dashboard?

Relevant equations a = delta a / delta t, Ff = uFn (i think)

The attempt at a solution I found out the minimum deceleration needed so that the cup falls over (a is < or = to -5.71) but i don't know how to find the coefficient of static friction

1 - I'm not sure why you introduce falling over. The question talks about sliding or not falling..
2 - When you say "I found the minimum acc..." it would be helpful to show how you did that.
3 - So, you calculated the acceleration for which the cup slides. Is the acceleration more or less, if you decelerate for a longer time?
4 - Can you calculate the force on the cup needed to produce this acceleration?

 

[haruspex]

Ff = uFn

It can be important to get this equation exactly right. In fact, there are two, one for static and one for kinetic. Note the difference:
$F_{kinetic}=\mu_kF_N$
$F_{static}\leq\mu_sF_N$