AP Physics – Friction (Static vs Kinetic, Coefficients)

AP Physics – Friction (Static vs Kinetic, Coefficients)

AP Physics: Friction (Static vs. Kinetic, Coefficients) – Exam-Ready Study Guide

What This Is

Friction is the force that resists motion between two surfaces in contact. It’s crucial on the AP exam because it appears in free-body diagrams, Newton’s laws problems, and energy/work questions. Without friction, cars wouldn’t stop, you couldn’t walk, and even writing with a pencil would be impossible. Historical example: The ancient Egyptians used logs as rollers to move massive stone blocks for the pyramids—reducing friction to make the job easier. On the AP exam, you’ll need to distinguish between static friction (prevents motion) and kinetic friction (opposes motion) and calculate their magnitudes using coefficients.

Key Terms & Concepts

• Friction (f): A contact force that opposes relative motion (or attempted motion) between two surfaces.
• Static Friction (fₛ): The frictional force that prevents an object from starting to move. Maximum static friction: fₛ,max = μₛN, where μₛ = coefficient of static friction, N = normal force.
• Kinetic Friction (fₖ): The frictional force acting on a moving object. Formula: fₖ = μₖN, where μₖ = coefficient of kinetic friction.
• Coefficient of Friction (μ): A dimensionless number (no units) that depends on the materials in contact. Typical values: μₛ > μₖ (e.g., rubber on concrete: μₛ ≈ 1.0, μₖ ≈ 0.8).
• Normal Force (N): The perpendicular force exerted by a surface on an object. On a flat surface, N = mg (if no vertical acceleration).
• Free-Body Diagram (FBD): A sketch showing all forces acting on an object. Key for friction problems!
• Newton’s First Law: An object stays at rest or in motion unless acted on by a net force. Static friction balances applied forces until fₛ,max is exceeded.
• Newton’s Second Law: Fₙₑₜ = ma. Used to solve for acceleration when friction is involved.
• Work Done by Friction: W = fₖ · d · cos(180°) = -fₖd (friction always does negative work).
• Rolling Friction: A special case where an object rolls without slipping (e.g., car tires). AP rarely tests this, but know it’s weaker than kinetic friction.

Step-by-Step: Solving Friction Problems

1. Draw a Free-Body Diagram (FBD):
2. Label all forces: mg (weight), N (normal), f (friction), and any applied forces (e.g., Fₚᵤₛₕ).
3. Static friction: Draw fₛ opposite the direction of intended motion.

4. Kinetic friction: Draw fₖ opposite the direction of actual motion.

5. Determine the Type of Friction:

6. Is the object moving? → Use fₖ = μₖN.

7. Is the object stationary but trying to move? → Use fₛ ≤ μₛN (static friction matches the applied force up to fₛ,max).

8. Resolve Forces:

9. Horizontal motion: Sum forces in the x-direction (Fₙₑₜ,x = ma).
10. Vertical motion: Sum forces in the y-direction (Fₙₑₜ,y = 0 if no vertical acceleration).

11. Example: If a box is pushed with force F on a flat surface:

    
    
    • x: F - fₖ = ma (if moving).
    • y: N - mg = 0 → N = mg.

12. Solve for the Unknown:

13. Plug in fₖ = μₖN or fₛ ≤ μₛN and solve for acceleration, force, or μ.

14. If static friction is involved: Check if fₛ,max is exceeded. If not, fₛ = Fₐₚₚₗᵢₑₑ (no acceleration).

15. Check Units and Reasonableness:

16. μ has no units.
17. f and N should be in Newtons (N).
18. Sanity check: If μ > 1, the surface is very rough (e.g., sandpaper). If μ < 0.1, it’s slippery (e.g., ice).

Common Mistakes

• Mistake: Assuming fₖ = μₖN always applies, even when the object is stationary.
  Correction: fₖ only applies to moving objects. For stationary objects, use fₛ ≤ μₛN and match fₛ to the applied force.

• Mistake: Forgetting that fₖ is constant, while fₛ varies up to fₛ,max.
  Correction: Static friction adjusts to balance applied forces until fₛ,max is reached. Kinetic friction is always μₖN.

• Mistake: Using mg instead of N in the friction formula.
  Correction: N is the normal force, which equals mg only on flat surfaces with no vertical acceleration. On an incline, N = mg cosθ.

• Mistake: Ignoring the direction of friction.
  Correction: Friction always opposes relative motion (or intended motion). If a box slides right, fₖ points left.

• Mistake: Rounding μ too early in calculations.
  Correction: Keep extra digits until the final answer to avoid rounding errors. AP graders deduct for significant figure mistakes!

AP Exam Insights

1. FRQ Hotspot: Friction appears in Newton’s laws FRQs (e.g., "A block is pushed on a surface with μₖ = 0.3. Calculate its acceleration.") and energy/work FRQs (e.g., "How much work does friction do as a sled slides 5 m?").
2. Multiple-Choice Trap: Questions may ask for fₛ,max but give μₖ instead. Read carefully!
3. Tricky Distinction: Static vs. kinetic friction. Static friction can be less than μₛN, but kinetic friction is always μₖN.
4. Inclined Planes: On ramps, N = mg cosθ, and friction opposes motion parallel to the surface. AP loves incline problems!

Quick Check Questions

1. Multiple Choice: A 10 kg box is at rest on a horizontal surface with μₛ = 0.5 and μₖ = 0.3. What is the maximum horizontal force that can be applied without moving the box?
2. (A) 30 N
3. (B) 49 N
4. (C) 50 N

5. (D) 98 N
   Answer: (B) 49 N. fₛ,max = μₛN = μₛmg = 0.5 × 10 × 9.8 = 49 N.

6. Short FRQ: A 5 kg block slides across a table with μₖ = 0.2. If it starts at 4 m/s, how far does it slide before stopping?
   Answer: 4.08 m. Use fₖ = μₖmg = ma → a = -μₖg = -1.96 m/s². Then v² = u² + 2as → 0 = 16 + 2(-1.96)s → s = 4.08 m.*

7. Multiple Choice: Which of the following is true about static friction?

8. (A) It is always equal to μₛN.
9. (B) It can be less than μₛN.
10. (C) It is always greater than kinetic friction.
11. (D) It depends on the object’s speed.
    Answer: (B) It can be less than μₛN. Static friction matches the applied force up to fₛ,max.

Last-Minute Cram Sheet

1. Static friction: fₛ ≤ μₛN (prevents motion).
2. Kinetic friction: fₖ = μₖN (opposes motion).
3. μₛ > μₖ for the same surfaces.
4. Normal force (N): N = mg on flat surfaces; N = mg cosθ on inclines.
5. Friction direction: Always opposes relative motion (or intended motion).
6. Work by friction: W = -fₖd (negative because force and displacement are opposite).
7. ⚠️ Don’t confuse fₖ and fₛ! Kinetic = moving, static = stationary.
8. ⚠️ On inclines, N ≠ mg! Use N = mg cosθ.
9. Units: μ is unitless; f and N are in Newtons (N).
10. AP loves: Free-body diagrams + Newton’s 2nd law with friction. Draw them first!