⚡Friction & Normal Force
Normal Force
The normal force is the force a surface exerts on an object, always perpendicular to the surface.
It's called "normal" because "normal" means perpendicular in math. When you stand on the floor, the floor pushes up on you — that's the normal force balancing your weight.
Normal force is NOT always equal to weight! If: - On a flat surface with no other vertical forces: N = mg - On a slope: N = mg cos θ - With a vertical push/pull: N = mg ± F_vertical (plus if pulling up, minus if pushing down)
Normal force adjusts to maintain contact — it can be zero (object leaves the surface) but never negative.
Friction
Friction is the force that opposes relative motion between surfaces in contact. It always acts parallel to the surface.
Static friction (f_s): prevents motion from starting. Can be anywhere from 0 to a maximum: f_s ≤ μ_s × N
Kinetic friction (f_k): acts when surfaces are sliding: f_k = μ_k × N
Where μ (mu) is the coefficient of friction — a dimensionless measure of surface roughness. Typical values: - Ice on ice: μ ≈ 0.03 - Wood on wood: μ ≈ 0.3 - Rubber on concrete: μ ≈ 0.8
Key fact: μ_s > μ_k (static friction is usually larger than kinetic friction — harder to start moving than to keep moving).
Free Body Diagram Practice — Friction Scenarios
Try "Block being pushed across floor" and "Block on ramp" in the FBD builder. Notice how friction always opposes motion, and the normal force is perpendicular to the surface.
Newton's Second Law Playground — Friction
Experiment with the friction coefficient μ. Set μ = 0 and watch constant acceleration. Increase μ until the block reaches terminal velocity. Use the incline to see gravity drive motion without any applied force.
Think About It
You push a 10 kg box with 30 N. If μ_s = 0.4 and μ_k = 0.3, does the box move? If yes, what is its acceleration?
✏️ Worked Example
Problem: A 20 kg box on a flat surface has μ_k = 0.25. A 60 N force pushes it horizontally. Find the acceleration. (g = 10 m/s²)
📐 Key Equations
Friction and Normal Force
f_s ≤ μ_s Nf_k = μ_k NN = mg\cosθ (on an incline at angle θ)⚠️ Common Mistakes
Misconception: Friction force always equals μN.
✓ Correct thinking: Kinetic friction always equals μ_k N. Static friction is at most μ_s N, but can be any value from 0 up to that maximum depending on the applied force.
Why: If you apply 5 N to a stationary box and μ_s N = 20 N, static friction is 5 N (just enough to keep it still), not 20 N.
Misconception: On an incline, the normal force equals mg (the full weight).
✓ Correct thinking: On an incline at angle θ, the normal force is N = mg cosθ — only the component of weight perpendicular to the surface.
Why: The normal force balances only the perpendicular component of gravity. Using the full weight overestimates N and therefore overestimates friction.
Misconception: Adding more weight to an object always makes it harder to slide because friction increases.
✓ Correct thinking: Friction does increase with more weight (f = μN = μmg), but the gravitational force along an incline also increases proportionally. On an incline, the ratio (and thus whether the object slides) depends only on μ and θ, not on mass.
Why: This is why all objects (regardless of mass) on a given surface slide at the same angle — the mass cancels out.
📝 Practice Problems
Try these problems. Check your answer when ready.
A 15 kg box rests on a flat surface. μ_s = 0.5, μ_k = 0.35. What is the minimum force needed to start the box moving? (g = 10 m/s²)
f_s,max = μ_s NOnce the box in the previous problem is moving (μ_k = 0.35), what force is needed to keep it moving at constant velocity?
A 10 kg block is on a surface with μ_k = 0.3. A horizontal force of 50 N is applied. Find the acceleration. (g = 10 m/s²)
A 5 kg block sits on a 37° incline (sin37° = 0.6, cos37° = 0.8). μ_k = 0.25. Does the block slide? If so, find its acceleration. (g = 10 m/s²)
You push a 20 kg box at 30° below horizontal with 80 N. μ_k = 0.3. Find the acceleration. (g = 10 m/s²)
A 3 kg block is on a surface with μ_s = 0.6. A horizontal force F is slowly increased from 0. At what exact applied force does the block begin to move? After that, μ_k = 0.4 and the applied force stays at the value that just started motion. What is the acceleration? (g = 10 m/s²)
A 2 kg block is on top of a 6 kg block. The bottom block is on a frictionless floor. μ_s between the two blocks = 0.4. A horizontal force F is applied to the bottom block. What is the maximum F before the top block starts sliding off? (g = 10 m/s²)
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