Put two objects together and increase the tilt until the top object slides. The critical angle &theta_c at which slipping occurs determines the static friction coefficient μ_s.

To relate the critical angle to μ_s, use DID TASC with f_s = f_{s max} = μ_s N.

1. Diagram and coordinate systems
2. Isolate the systems
3. Draw all forces acting
4. Take components
5. Apply F=ma and constraints
6. Solve
7. Check!

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 θ_c into the left equation gives:
mg sin θ_c = μ_s mg cos θ_c   or   tan θ_c= &mu_s

A similar method gives μ_k. Adjust the angle so that a pushed object continues to slide with constant speed. When this occurs, the tangent of the angle equals μ_k.