Statics — Forces & Equilibrium

Friction — will it slide?

continues from lesson 5 — values defined earlier in the course stay live here

ELI5: friction resists sliding up to a limit, f_max = μ·N, where N is how hard the surfaces press together. Push below that limit and nothing budges; exceed it and the object breaks free. It's a threshold, not a fixed force.

g_{acc} := 9.81 m/s^2

= 9.81 m / s^2 gravity

m_{crate} := 50 kg

= 50 kg a crate on the floor

N_{normal} = m_{crate} \cdot g_{acc}

= 490.5 (kg m) / s^2 the floor pushes back with this

\mu_{s} = 0.4

static friction coefficient (rubber on concrete-ish)

f_{max} = \mu_{s} \cdot N_{normal}

= 196.2 (kg m) / s^2 the most friction available ≈ 196 N

F_{shove} := 150 N

= 150 N how hard you push

✓ pass

F_{shove} < f_{max}

TRUE → the crate stays put (push harder than 196 N to move it)

Real-world hook: μ·N is why car brakes have a limit (skidding), why bolted joints hold by clamping, and how a conveyor grips its load.

Try it yourself: the maximum friction on an 80 kg crate with μ = 0.3? (f = μ·m·g, use g = 9.81 m/s².)

fmax_{you} := 0.3 * 80 kg * 9.81 m/s^2

= 235.44 N ✏️ Your turn: multiply μ = 0.3 by the weight (80 kg × 9.81 m/s²).

✓ pass

abs(fmax_{you} - 0.3 * 80 kg * 9.81 m/s^2) < 0.01 N

green when your maximum friction force is correct

Where next: Mechanics of Materials takes these forces inside the material — turning a load into the stress that decides whether a part survives.