Topic 2.7: Kinetic and Static Friction

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Before We Start: Think About It

It's hardest to get a heavy couch moving, but once it's sliding, it actually feels a little easier to keep going. What do you think causes that?

Today's New Concepts

AP CED Alignment: Unit 2, Topic 2.7

Kinetic Friction

• Occurs when two surfaces ARE sliding relative to each other
• Opposes the direction of relative motion
• Does NOT depend on the surface area of contact — only on the normal force and the materials involved
• $F_{f,k} = \mu_kF_N$, where $\mu_k$ is the coefficient of kinetic friction

Worked Example: A 15 kg box slides with $\mu_k=0.25$: $F_N = mg = 147\text{ N}$, so $F_{f,k} = (0.25)(147) \approx 37\text{ N}$.

Static Friction — Self-Adjusting, Not Fixed

• Occurs when surfaces are NOT sliding relative to each other
• Adjusts itself to whatever value is needed to prevent slipping — it is NOT automatically at its maximum
• Maximum value: $F_{f,s,max} = \mu_sF_N$; only reached at the exact instant slipping is about to begin
• $\mu_s$ is typically greater than $\mu_k$ for the same two surfaces — this is why friction briefly drops the instant something starts sliding

Worked Example: A 10 kg crate at rest, $\mu_s=0.40$, has a 20 N force applied and doesn't move: actual friction is 20 N (matches the applied force), while the maximum available is $\mu_sF_N=(0.40)(98)=39.2\text{ N}$ — well above 20 N, so the crate isn't close to slipping.

Multiple Friction Interfaces

• When objects are stacked, each contact surface has its own normal force, based on the total weight it has to support — not just the object directly touching it
• Adding weight anywhere in a stack changes the normal force (and friction) at every interface below that weight

Worked Example: Box A (mass $m$) sits on Box B (mass $2m$), which sits on the floor. Friction at A-B: $F_{f,1}=\mu_1mg$ (only supports A). Friction at B-floor: $F_{f,2}=\mu_2(3mg)$ (supports the whole stack).

Keep This Sheet!

These sheets build into your semester study guide. Keep them in order in a binder or folder — you'll want to flip back through them before quizzes, unit tests, and when AP exam review starts in the spring.