Friction, Part 1
The basic action of friction. Where friction comes from, static friction up to \(\mu_s N\) and kinetic friction \(\mu_k N\). Then the graph of friction against the push, the rough incline and the angle of repose, and walking, cycling and braking.
Why this chapter
Push a heavy almirah and it refuses to move, then lurches. A ball rolled along the pitch stops by itself. A car on a wet road takes twice as far to stop. Every one of these is friction, the force that the last three chapters mostly left out. Friction is also the force that lets you walk at all. This chapter builds the basic action of friction. It covers where friction comes from, its two kinds and the one graph that holds them both. Then it treats the block on a slope and the friction that moves people and vehicles.
You will learn
- Explain where friction comes from and find its direction, against the sliding or against the tendency to slide.
- Find static friction from equilibrium, and use the limit \(f_s \le \mu_s N\) and the kinetic value \(f_k = \mu_k N\).
- Read the graph of friction against the applied force, and solve any push on a block on a level floor.
- Solve a block on a rough incline at rest, on the point of sliding, sliding down and pushed up, and use \(\tan\theta = \mu_s\).
- Say which way friction points on a walking foot, a driving wheel and a braked wheel, and find stopping distances.
Before you begin
You should be able to draw a free-body diagram and apply Newton's first and second laws to a single body. You should be able to use Newton's third law to name the pair of a force. You should also be able to split a force into components along and at right angles to a slope.
Lessons
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%Glossary
The key words of this chapter, with the meaning this chapter gives them.
- angle of repose
- The largest angle of an incline on which a body can rest without sliding. It satisfies \(\tan\theta_r = \mu_s\).
- coefficient of kinetic friction
- The ratio of kinetic friction to the normal reaction, \(\mu_k\). It is always smaller than \(\mu_s\) for the same pair of surfaces.
- coefficient of static friction
- The ratio of limiting friction to the normal reaction, \(\mu_s\). A pure number set by the pair of surfaces.
- contact force
- A force that acts only while two bodies touch, such as the normal reaction and friction. It vanishes when the surfaces separate.
- driving wheel
- A wheel turned by the engine or the pedals. Its tyre pushes the road backward, so road friction on it points forward.
- friction
- The force along the surface of contact that one surface exerts on another. It resists the sliding of one surface over the other.
- kinetic friction
- The friction between two surfaces sliding over each other. It has the fixed value \(\mu_k N\) and points against the relative velocity.
- limiting friction
- The largest possible static friction, reached when a body is on the point of sliding. It equals \(\mu_s N\).
- normal reaction
- The contact force at right angles to the surface of contact, pressing the two surfaces apart. Written \(N\).
- relative motion
- The motion of one body as seen from another. Friction depends on the motion of one surface relative to the other surface, not relative to the ground.
- rolling friction
- The resistance to rolling that comes from the slight denting of a wheel or ball and the surface under it. It is usually much smaller than sliding friction.
- skidding
- The sliding of a tyre over the road when a wheel locks or spins. A skidding tyre feels kinetic friction, smaller than the static friction of a rolling tyre.
- static friction
- The friction between two surfaces that do not slide over each other. It adjusts itself to balance the other forces along the surface, up to a limit.