50
N
0.5
50
N
30
N
20
N
1.6667
50
N
0.5
50
N
30
N
20
N
1.6667
Friction is the resistive force that opposes relative motion or the tendency of motion between two surfaces in contact. It is calculated using Coulomb's friction model: $$f = \mu N$$, where $$\mu$$ is the coefficient of friction and $$N$$ is the normal force. There are two types: static friction ($$f_s \leq \mu_s N$$), which prevents motion from starting, and kinetic friction ($$f_k = \mu_k N$$), which opposes sliding motion already in progress.
Static friction is variable — it matches the applied force up to a maximum value $$\mu_s N$$. Once this maximum is exceeded, the object begins to slide and kinetic friction takes over. Crucially, the kinetic coefficient is almost always less than the static coefficient ($$\mu_k < \mu_s$$), which is why it is harder to start pushing a heavy object than to keep it moving.
This calculator lets you switch between static and kinetic friction and computes the friction force for any given normal force and coefficient. It is essential for engineering problems involving brakes, tires, conveyor belts, bolted joints, and any system where surfaces interact.
The friction force is computed using Coulomb's friction law:
Static friction (maximum): $$f_{s,max} = \mu_s \times N$$
Kinetic friction: $$f_k = \mu_k \times N$$
The coefficient of friction $$\mu$$ is dimensionless and depends on the material pair and surface condition. Typical values range from 0.01 (ice on ice) to over 1.0 (rubber on concrete). The normal force $$N$$ is the perpendicular contact force, which on a flat surface equals $$mg$$.
Note: the static friction formula gives the maximum possible static friction. Actual static friction can be any value from zero up to this maximum, exactly matching the applied parallel force until the threshold is exceeded.
A higher friction force means greater resistance to sliding. If your applied force exceeds the maximum static friction, the object starts moving and kinetic friction applies. Compare static and kinetic results to see the 'breakaway' effect — the force needed to start motion is greater than the force needed to sustain it.
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A 50 kg crate (N = 490 N) requires over 303.8 N to start sliding on concrete.
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Results
Once moving, friction drops to 235.2 N — about 22% less force needed to keep it sliding.
Static friction acts on objects at rest, preventing them from starting to move. It can range from zero up to a maximum of $$\mu_s N$$. Kinetic friction acts on objects already in motion and has a constant value of $$\mu_k N$$. Static friction is generally larger than kinetic friction for the same surface pair.
At rest, surface irregularities (asperities) interlock more completely, and molecular adhesion bonds have time to form. Once sliding begins, contact points are continuously broken before full bonding occurs, resulting in lower resistance. This is why heavy furniture 'jerks' when you first push it, then slides more easily.
Engineering handbooks (Marks', Machinery's Handbook) and material databases provide $$\mu$$ values for common material pairs. Typical examples: rubber on dry concrete 0.6-0.8, steel on steel 0.6-0.8 (dry) or 0.05-0.1 (lubricated), Teflon on steel 0.04-0.05, ice on ice 0.01-0.05.
In the Coulomb model, friction does not depend on contact area — only on normal force and the coefficient. This is because larger area distributes the force over more asperities, but each asperity bears less load, and the effects cancel. At extreme scales or with soft materials, some area dependence can appear.
Yes. Some material pairs, like rubber on rough concrete, have coefficients exceeding 1.0 (sometimes up to 1.5). This simply means the friction force exceeds the normal force, which is perfectly physical and occurs with highly adhesive or interlocking surfaces.
Rolling friction (rolling resistance) occurs when a circular object rolls on a surface. It is much smaller than sliding friction and is characterized by a rolling resistance coefficient. This calculator covers sliding friction only; rolling friction requires a different model involving deformation and hysteresis.
Roboculator Team
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