A2 notes: Friction
Resistance to motion
Have you ever noticed that, when you try to slide something heavy along a surface, there is a momentary feeling of extra resistance before the object starts to move?
If so, you have experienced the difference between static and dynamic friction.
What exactly is friction?
At its simplest, it's the resistance to movement between two surfaces that are in full contact with each other.
It can be both a hindrance and a help depending on the circumstances. For example, suppose, while moving house, you have a box of books that is too heavy to carry for any distance and needs to be slid along the floor. In that case, friction manifests itself as a resistant force in opposition to the propulsive force. The magnitude of the frictional force is proportional to the ‘normal’ force, which is the reaction by the floor against the force of gravity on the box: the weight of the box, in other words. Adding more books increases the frictional force and therefore the resistance to movement. Removing books reduces the weight of the box, consequently decreasing the normal reaction force, and subsequently the resistance to movement. On the other hand, it's nicer to move house on a dry rather than icy day.
Coefficient of friction
The constant of proportionality in the relationship between the friction force and the normal force is the coefficient of static or dynamic friction, depending on whether the box is stationary or moving, respectively. It is usually denoted as \(μ _\text{s}\) or \(μ _ \text{d}\). The normal force is always perpendicular to the contact surface. The frictional force is always parallel to the contact surface and opposite in direction to any propulsive force.
It should be noted that the relevant equation, \(F_\text{f} = μ F_\text{N}\), is linear since \(F_\text{f}\) and \(F_\text{N}\) are always perpendicular to each other and represent the magnitudes of the forces.
Where the two surfaces are stationary with respect to each other, \(F_\text{f} \le μ_\text{s} F_\text{N}\), where \(F_\text{f}\) is at its maximum possible value immediately before the point of movement between the surfaces.
And, where the surfaces are in relative motion, the dynamic frictional force having been exceeded by the motive force is \(F_\text{f} = μ_\text{d} F_\text{N}\).
\(μ _\text{s}\) is usually, though not always, higher than \(μ _ \text{d}\). The reason is that maximum resistance is greater when the surfaces are locked together by molecular forces, or asperities (microscopic protrusions), creating grip or traction. The coefficient of friction, static or dynamic, requires there to be two surfaces. They could be steel on ice, wood on wood, or glass on glass, and so on, and needs to be determined experimentally, as it depends on the particular nature of the materials and whether or not they are in relative motion.
.png)
Friction in the world
Incidentally, where an object is sliding down a slope, under the influence of gravity, without any acceleration (because the magnitude of the upslope frictional force equals the downslope component of the object’s weight), it can be shown that the coefficient of friction equals the tangent of the angle of inclination of the slope:
Since \(F_\text{g} \sin θ = μ F_\text{N} = μF_\text{g} \cosθ\), (where \(F_\text{g}\) is the weight of the sliding object),
\(μ = {\sin θ\over \cos θ} = \tan θ\)
In this scenario, somewhat counterintuitively, the resistance due to the frictional force between two surfaces has nothing to do with the macroscopic contact area. It just takes a few microscopic bumps for two surfaces to be in contact and create a higher coefficient of friction between two highly polished sheets of steel, for example, than, let's say, two sheets of wood. This is the reason we use oil as an engine lubricant.
It's worth noting that unless they are locked due to braking, rolling wheels are, at the point of contact, instantaneously at rest with respect to the surface of interaction. They therefore experience static friction, even if the vehicle they are part of is moving.
As to the advantages and disadvantages of friction, both emerge from the same phenomena! No one would argue that the shrieking of car brakes is as beautiful as the sound of a well-played violin, yet both result from rapidly alternating static and dynamic friction. But, while a downhill skier needs their skis to be waxed to reduce friction on the slopes, a surfer needs their board to be regularly waxed so they don't slip off!
Whilst most pairs of materials have a slightly higher coefficient of static friction than dynamic friction, one substance where this is not the case is polytetrafluoroethylene, more commonly known as PTFE, or teflon. Teflon on teflon has a very low coefficient of both static and dynamic friction, which is why it's so commonly used for things like non-stick pan coatings or low friction bearings. However, possibly the most interesting fact about PTFE is that it's the only known substance that geckos are unable to grip with their sticky spatula-like feet!
Images
- Skier skiing downhill in high mountains photo by Ulvi Safari on Unsplash
- Friction surface microstructure by Colinvella, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
- Friction graph by Maxmath12, CC0, via Wikimedia Commons
- Mountain biking photo by Santiago Pazos Bordon on Unsplash
- A frying pan filled with eggs and vegetables photo by Rob Wicks on Unsplash