The friction force is a contact force that opposes the motion, or the tendency toward motion, of one object relative to another. It depends on the nature of the materials in contact and on the force pressing them against each other.
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How to measure it in class
You do not measure a friction force with a smartphone sensor: you deduce it from a motion. Two complementary methods are available, the sliding angle and video analysis.
Steps:
- Inclinometer method: place the object on a board, place the smartphone on the same board and open FizziQ’s inclinometer
- Tilt very slowly until the precise instant when the object starts to slide, and record the angle α; you then have μ_s = tan α
- Repeat five to ten times and take the average, because the scatter is large
- Kinematic method: film the object as it slides or rolls, with a graduated ruler in the field of view
- Mark the positions frame by frame in FizziQ’s video analysis module and plot v as a function of t
- The deceleration a is read from the slope; on a horizontal plane, μ_d = a/g, and on a plane inclined at an angle θ, μ_d = (g sin θ − a)/(g cos θ). Allow at least half a second of sliding, otherwise a video at 30 frames per second does not provide enough points
Scientific activities on this topic
- Ballistics with air resistance - compare a real trajectory to the ideal parabola and measure the deviation due to air resistance
- Inclined plane: weight components - project the weight onto the plane and bring out the role of the normal reaction
- Aerodynamics of a badminton shuttlecock - observe by video analysis a trajectory strongly slowed by drag
- Pendulum: the relation a = 2gh/r - measure the progressive damping due to friction over several oscillations
Learn more
Coulomb’s laws of solid friction
Formulated by Amontons at the end of the 17th century and then established experimentally by Charles-Augustin Coulomb in 1785, they are stated in three points:
- The friction force is proportional to the normal pressing force N, not to the weight: on an inclined plane, N = mg cos θ, not mg.
- It is independent of the area of the contact surface.
- In the sliding regime, it is independent of the speed.
Points 2 and 3 are counter-intuitive and deserve discussion in class. Placing a brick on its large face or on its edge changes nothing about the force needed to make it slide. The explanation lies in the difference between apparent surface and real contact surface: at the microscopic scale, the two solids only touch at the tips of their asperities, over a tiny area which, for its part, is proportional to N. Doubling the apparent surface halves the pressure and leaves the product unchanged.
These laws are approximations, and clearly so: they fail for racing tires (where surface area matters), at very high pressures, at very high speeds, or for soft materials. But they correctly describe the vast majority of situations, and they are the ones taught in the high school physics curriculum.
Static and dynamic: the threshold
Static friction has no value of its own: it is an adaptive force. If you push a wardrobe with 50 N and it does not move, the friction is exactly 50 N. With 100 N and no motion, it is 100 N. It only stops growing when it reaches its ceiling μ_s·N; beyond that, sliding begins and the force drops abruptly to μ_d·N, which is lower. This drop-off explains the jerky sensation when moving a piece of furniture, the squeal of a chalk stick, and the sound of a violin bow, which alternates thousands of times per second between sticking and sliding.
Fluid friction: a different regime
An object moving through air or water experiences a drag whose law depends on the flow regime. At low speed or for very small objects (laminar flow), the force is proportional to the speed: F = k·v. At the speeds common in high school mechanics (turbulent flow), it is proportional to the square of the speed:
F = ½ ρ C_x S v²
Here there is no threshold, and no independence from speed or surface: the exact opposite of solid friction. A direct consequence is the terminal velocity: a falling body accelerates until drag balances weight, then falls at constant speed. A skydiver in free fall reaches about 200 km/h with arms and legs spread, and 5 m·s⁻¹ with the canopy open, with nothing but S and C_x having changed.
Useful friction, harmful friction
The classroom reflex is to see friction as a nuisance. That is wrong in half of the cases. Without static friction we could not walk, drive a car forward, tighten a knot, or hold an object in the hand: a tire rolling without slipping is a case of grip, not of sliding, and it is this grip that propels the vehicle. Brakes, clutches and climbing ropes rely entirely on friction. Conversely, it is costly wherever free motion is wanted: roughly one third of the fuel of a combustion-engine vehicle is lost to friction, hence ball bearings and lubricants.
Where the energy goes
The work done by a friction force is always negative in the sliding regime: W = −f·d. Mechanical energy is therefore not conserved; it is converted into heat and, to a small extent, into sound and wear. This is what distinguishes friction from conservative forces such as weight: the balance depends on the path followed, not only on the start and end points.
Formula
Static friction, as long as there is no sliding:
f ≤ μ_s · N
Dynamic friction, in the sliding regime:
f = μ_d · N with μ_d < μ_s
Normal reaction on a plane inclined at an angle θ:
N = m g cos θ
Static coefficient deduced from the limiting sliding angle α:
μ_s = tan α
Fluid drag in the turbulent regime:
F = ½ ρ C_x S v²
Work done by a friction force over a distance d:
W = − f · d
where:
- f: magnitude of the friction force (N)
- N: normal component of the support reaction (N)
- μ_s: coefficient of static friction (dimensionless)
- μ_d: coefficient of dynamic friction (dimensionless)
- α: tilt angle at the moment sliding begins (°)
- ρ: density of the fluid, 1.2 kg·m⁻³ for air (kg·m⁻³)
- C_x: drag coefficient, dimensionless (about 0.3 for a car, 0.47 for a sphere)
- S: frontal cross-sectional area of the object (m²)
- v: relative speed of the object in the fluid (m·s⁻¹)
Application examples
- A 20 kg crate resting on concrete (μ_s ≈ 0.6): you must exceed f = 0.6 × 20 × 9.81 ≈ 118 N to get it moving. Once started, with μ_d ≈ 0.5, only 98 N are needed to keep it moving.
- Orders of magnitude of the coefficients: rubber on dry concrete, 0.7 to 1.0; steel on steel, 0.6 dry and 0.1 lubricated; ski on snow, 0.05; ice on ice, 0.03; human synovial joint, 0.003 - one of the least frictional contacts known.
- Emergency braking on a dry road: the maximum deceleration is a = μg ≈ 0.8 × 9.81 ≈ 7.8 m·s⁻². From 90 km/h (25 m·s⁻¹), the braking distance is d = v²/(2a) ≈ 40 m. On a wet road, μ drops toward 0.4 and the distance doubles.
- A badminton shuttlecock is the most heavily braked projectile in any sport: its conical skirt gives it a very high C_x for a mass of 5 g, so that its trajectory, far from being parabolic, drops almost vertically at the end of its flight.
- A steel ball dropped into glycerol reaches within a few centimeters a terminal velocity of a few cm·s⁻¹: here the regime is laminar and the drag is proportional to v (Stokes’ law).
- On a track inclined at 25°, an object remains stationary if μ_s > tan 25° = 0.47: hence the limiting angle of about 30° for slopes of granular materials.
FAQ
Q: Why does the friction force not depend on the contact surface? A: Because the surface actually in contact is not the apparent surface. The two solids only touch at the tips of their microscopic asperities, and this real area is proportional to the pressing force, not to the size of the face resting on the surface. Doubling the apparent surface halves the pressure: the product does not change. It is an approximate law, but a very robust one for common solids.
Q: Why is it harder to get a piece of furniture moving than to keep pushing it afterwards? A: Because μ_s > μ_d. As long as the object is stationary, static friction can rise up to μ_s·N. As soon as sliding begins, the force drops to μ_d·N, which is lower. The difference is typically 10 to 30 %.
Q: Does friction really depend on speed? A: For solid friction, no - to a first approximation, that is Coulomb’s third law. For fluid friction, yes, and strongly: drag grows as v² at usual speeds. Confusing the two regimes is the most frequent error in this chapter.
Q: Can a friction coefficient exceed 1? A: Yes. A μ greater than 1 simply means that you must push harder than the weight to make the object slide. Soft rubber on clean asphalt reaches 1.2 to 1.5, and some racing tires exceed 1.7.
Q: Where does the energy lost to friction go? A: Essentially into heat in the two surfaces, with a small share into sound and wear of the material. It is mechanical energy converted into thermal agitation, a disordered form that cannot be fully recovered. Total energy, for its part, is indeed conserved.
Related concepts
Inclined Plane - Mechanical Energy - Terminal Velocity - Conservation of Energy