Put two objects together and increase the tilt until the top object slides. The critical angle &thetac at which slipping occurs determines the static friction coefficient μs.
To relate the critical angle to μs, use DID TASC with fs = fs max = μs N.
Steps 1-4: See diagram and transparency
Step 5: Apply Newton's 2nd law
|ΣFx = m ax = 0|||||ΣFy = m ay = 0|
|mg sin θc - fs = 0|||||N - mg cos θc = 0|
|mg sin θc = μs N|||||N = mg cos θc|
Step 6: Solve
Substitute for N= mg cos θc into the left equation gives:
mg sin θc = μs mg cos θc or   tan θc= &mus
A similar method gives μk. Adjust the angle so that a pushed object continues to slide with constant speed. When this occurs, the tangent of the angle equals μk.