How do i find the coefficient of static friction?

AI Thread Summary
To find the coefficient of static friction between a coffee cup and a dashboard, it's essential to calculate the maximum deceleration that prevents the cup from sliding. The relevant equations include acceleration (a = delta a / delta t) and the frictional force (Ff = uFn). The discussion highlights that the cup slides when deceleration exceeds -5.71 m/s², and emphasizes the need to differentiate between static and kinetic friction equations. Additionally, calculating the force acting on the cup during deceleration is crucial for determining the coefficient of static friction. Understanding these concepts will lead to the correct solution for the problem.
sam kim
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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
 
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sam kim said:
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?
 
sam kim said:
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##
 

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