Physics › 🚀 Mechanics

Forces & Friction

Why it takes a harder shove to start a stuck crate sliding than it does to keep it gliding — and how one number, μ, predicts the whole story.

High schoolAP Physics 1 level
💡
The big idea: A force is just a push or pull between two objects, and a free-body diagram is how you keep every one of them straight. Friction is a special contact force that resists relative sliding, and it obeys a beautifully simple rule — F = μN — where the normal force N does the real work of setting how hard the surfaces are pressed together. Static friction adapts up to a maximum before an object breaks free; kinetic friction, once sliding, settles into something smaller and steadier.
🎯 By the end, you'll be able to
  • Draw and interpret free-body diagrams that correctly identify every force acting on an object, including the normal force.
  • Distinguish static friction from kinetic friction and explain why the maximum static friction is usually greater than the kinetic friction force.
  • Apply F = μN to calculate friction forces on flat surfaces and on inclines.
  • Predict whether an object on an incline stays put or starts sliding by comparing tanθ to the coefficient of static friction.
📎 You should already know
  • Newton's Laws of Motion
  • Vectors and vector components
  • Basic trigonometry (sine, cosine, tangent)

What a force actually is

A force is nothing mysterious — it's a push or a pull that one object exerts on another, always as part of a pair. Lean on a wall and the wall leans back on you exactly as hard; that's Newton's third law quietly at work. To keep track of every force acting on a single object, physicists draw a free-body diagram: the object shown as a dot, with an arrow for each force on it — gravity pulling down, a normal force pushing perpendicular to whatever surface it touches, maybe an applied push, and friction resisting any sliding. Get the diagram right and the rest of the problem is just adding up arrows.

🔑 The normal force isn't fixed — it reacts

The normal force \(N\) is a surface's way of refusing to let an object pass through it. It always points perpendicular to the surface, and its size is whatever is needed to stop the object from accelerating into that surface — it is not automatically equal to weight. Press down on a book resting on a table and the normal force grows to match; tilt that table into a ramp and the normal force shrinks to \(mg\cos\theta\), because now only part of gravity presses into the surface.

\[ F_{friction} = \mu N \]
Friction is proportional to the normal force pressing two surfaces together. μ (mu), the coefficient of friction, depends on what the two materials are — not on speed, and not on how much surface area is touching.
\[ F_s \le \mu_s N \quad \text{(static)} \qquad\qquad F_k = \mu_k N \quad \text{(kinetic)} \]
Static friction is a range: it supplies whatever force is needed to prevent sliding, up to a maximum of μsN. Kinetic friction, once something is actually sliding, settles at a fixed value μkN. Since μs is usually a little larger than μk, it always takes more force to start something moving than to keep it moving.
\[ N = mg\cos\theta \qquad\qquad F_{\parallel} = mg\sin\theta \]
On an incline tilted at angle θ, gravity splits into a component pressing into the ramp (mg cosθ, which sets N) and a component pulling the object down the slope (mg sinθ, which friction must resist).
🎮 Interactive: Push, stick, then slide LIVE
Drag the applied force up from zero and watch the block resist without moving — then break free once you exceed μsN. Notice the force needed to keep it sliding at constant speed is smaller than the force it took to start it.
📝 Worked example: A 10 kg crate rests on a horizontal floor. The coefficient of static friction is μs = 0.40 and the coefficient of kinetic friction is μk = 0.30. (a) What horizontal force is needed to just start the crate moving? (b) Once it's sliding, what force keeps it moving at constant velocity? (Use g = 9.8 m/s².)
  1. Find the normal force: the floor is horizontal with no other vertical force, so N = mg = 10 kg × 9.8 m/s² = 98 N.
  2. Maximum static friction sets the breakaway force: F_s,max = μs N = 0.40 × 98 N = 39.2 N. Any push weaker than this and static friction just matches it, keeping the crate still.
  3. Once sliding, kinetic friction takes over: F_k = μk N = 0.30 × 98 N = 29.4 N. To hold constant velocity (zero acceleration), the applied force must exactly balance this.
✓ About 39.2 N is needed to start the crate moving, but only about 29.4 N keeps it sliding at constant speed — noticeably less, which is why a stuck box seems to 'give' all at once.
📝 Worked example: A wooden crate sits on a ramp tilted at 30° above horizontal. μs = 0.30 and μk = 0.25. (a) Does the crate slide on its own? (b) If it's given a nudge and starts sliding, what is its acceleration down the ramp? (Use g = 9.8 m/s².)
  1. Test whether it slides on its own by comparing tanθ to μs: tan(30°) = 0.577. Since 0.577 > μs = 0.30, the component of gravity along the slope beats the maximum static friction — the crate cannot stay put and slides on its own.
  2. Once sliding, find the net force along the ramp: F_net = mg sinθ − μk mg cosθ = mg(sinθ − μk cosθ).
  3. Plug in numbers: sin 30° = 0.500, cos 30° = 0.866, so a = g(sinθ − μk cosθ) = 9.8 × (0.500 − 0.25 × 0.866) = 9.8 × (0.500 − 0.2165) = 9.8 × 0.2835 ≈ 2.78 m/s².
✓ Yes — since tanθ (0.577) exceeds μs (0.30), the crate slides on its own, and once moving it accelerates down the ramp at about 2.8 m/s².
⚠️ Common mix-up: friction is not about surface area

It's tempting to think a wider tire or a bigger crate base means more friction — it doesn't, at least not in this ideal model. \(F = \mu N\) only cares about the normal force pressing the surfaces together and the roughness pairing \(\mu\); contact area doesn't appear in the equation at all. Also, don't assume friction always points 'backward' relative to travel — it opposes relative sliding at the surface, which is why static friction can point uphill, downhill, or sideways depending on what's trying to make the object slip.

Check your understanding

1. Which statement best describes the normal force?
The normal force is a reaction force perpendicular to the surface of contact. Its magnitude isn't fixed — it adjusts (for example, to mg on a flat floor, or mg cosθ on an incline) to whatever is needed to prevent the object from passing through the surface.
2. A 5 kg block sits on a table with μs = 0.50. Using g = 9.8 m/s², what is the maximum static friction force before the block starts to slide?
N = mg = 5 kg × 9.8 m/s² = 49 N. Maximum static friction is F_s,max = μs N = 0.50 × 49 N = 24.5 N.
3. Why doesn't the size of the contact area appear in F = μN?
In the standard model of friction, F = μN captures how hard the surfaces press together and how rough that particular pairing is. Doubling the contact area while keeping the same normal force spreads that same force over more area without changing the total friction force.
4. A crate sits on a ramp inclined at 20° with μs = 0.45. Will it start sliding on its own?
An object stays put when the gravity component along the slope (mg sinθ) doesn't exceed the maximum static friction (μs mg cosθ) — equivalently, when tanθ ≤ μs. Here tan(20°) ≈ 0.36, which is less than μs = 0.45, so the crate remains still. Mass cancels out of this comparison entirely.
✅ Key takeaways
  • The normal force adjusts to whatever is needed to keep an object from passing through a surface — it isn't always equal to weight.
  • Friction has two regimes: static friction (variable, up to a maximum of μsN) holds objects still, while kinetic friction (roughly constant, μkN) takes over once sliding begins.
  • F = μN means friction depends on how hard two surfaces are pressed together and how rough that pairing is — not on contact area, and not on speed.
  • On an incline, compare tanθ to μs: if tanθ exceeds μs, the object slides on its own; if not, static friction holds it in place.