Describe solid friction as the force between two surfaces that may impede motion and produce heating
1.5.1 Effects of Forces – Solid Friction
Learning Objective
Describe solid friction as a contact force between two solid surfaces that may impede motion and that can produce heating.
What Is Solid Friction?
Solid friction is the resistive contact force that arises when two solid surfaces are in touch. It always acts opposite to the direction of relative motion (or the tendency for motion). It can:
- Prevent an object from starting to move – static friction.
- Oppose the motion of an object that is already sliding – kinetic (sliding) friction.
- Convert mechanical energy into thermal energy, heating the contacting surfaces.
Types of Solid Friction
- Static friction (\$f_s\$) – acts while the surfaces are at rest relative to each other.
It can take any value from zero up to a maximum:
\$f{s,\max}= \mus\,R\$
Only when the applied force exceeds \$f_{s,\max}\$ will the bodies start to slide.
- Kinetic (sliding) friction (\$f_k\$) – acts once the surfaces are sliding.
Its magnitude is (generally) constant:
\$fk = \muk\,R\$
Mathematical Description
The magnitude of the frictional force is proportional to the normal reaction \$R\$ between the surfaces:
\$f = \mu\,R\$
where
- \$f\$ – frictional force (N)
- \$\mu\$ – coefficient of friction (dimensionless)
- \$R\$ – normal reaction (N)
Two coefficients are used:
- \$\mus\$ – coefficient of static friction (used in \$f{s,\max}= \mu_s R\$)
- \$\muk\$ – coefficient of kinetic friction (used in \$fk = \mu_k R\$)
Factors Influencing Friction
- Nature of the surfaces: Rougher or more “sticky’’ surfaces give a larger \$\mu\$ → larger \$f\$.
- Normal reaction (\$R\$): Increasing \$R\$ increases \$f\$ directly because \$f\propto R\$.
- Apparent area of contact: For rigid, solid surfaces the macroscopic contact area has little effect on \$f\$; the real microscopic contact area determines \$\mu\$.
- Speed of sliding: In the IGCSE syllabus \$\mu_k\$ is treated as constant, although in practice it may vary slightly with speed.
Typical Coefficients of Friction
| Pair of Surfaces | Static \$\mu_s\$ | Kinetic \$\mu_k\$ |
|---|---|---|
| Rubber on dry concrete | 0.9 | 0.8 |
| Wood on wood (dry) | 0.5 | 0.4 |
| Steel on steel (dry) | 0.6 | 0.4 |
| Ice on ice | 0.1 | 0.03 |
Heating Effect of Friction
When friction does work, mechanical energy is transformed into internal energy (heat), raising the temperature of the surfaces.
Work done by friction over a distance \$d\$:
\$W_f = f\,d\$
If all this work becomes heat \$Q\$, the temperature rise of a body of mass \$m\$ and specific heat capacity \$c\$ is:
\$Q = mc\Delta T \;\;\Longrightarrow\;\; \Delta T = \dfrac{f\,d}{m c}\$
Example: Brake pads and discs become hot because kinetic friction converts the car’s kinetic energy into heat.
Practical Investigation – Determining the Coefficient of Friction
Apparatus: smooth wooden block, smooth horizontal surface, spring balance, set of masses, ruler.
Method (horizontal‑pull):
- Place the block on the horizontal surface.
- Attach the spring balance to the block and pull slowly until the block just begins to move. Record the reading \$F_{s,\max}\$.
- Continue pulling at a constant speed and record the steady reading \$F_k\$.
- Measure the normal reaction \$R = mg\$ (mass of block \$m\$ plus any additional masses).
- Calculate \$\displaystyle\mus = \frac{F{s,\max}}{R}\$ and \$\displaystyle\muk = \frac{Fk}{R}\$.
Observations to note: \$\mus\$ is always larger than \$\muk\$, and the values are independent of the apparent contact area of the block.
Real‑World Examples
- Sliding a book across a table – kinetic friction opposes the motion.
- Pushing a heavy box – static friction must be overcome before it starts moving.
- Car tyres on a road – static friction provides the grip needed for acceleration, cornering and climbing.
- Braking a bicycle – kinetic friction between brake pads and rim converts kinetic energy into heat.
Key Points to Remember
- Friction is a contact force that always acts opposite to the direction of relative motion or the tendency for motion.
- Static friction can take any value from \$0\$ up to a maximum \$f{s,\max}= \mus R\$; kinetic friction has a (approximately) constant value \$fk = \muk R\$.
- The equation \$f = \mu R\$ applies to both static (using \$\mus\$) and kinetic (using \$\muk\$) friction, and \$\mu\$ is dimensionless.
- Heating is a direct consequence of the work done by friction: \$W_f = f d \;\rightarrow\; \Delta T = \dfrac{f d}{m c}\$.
- For most solid, rigid surfaces the apparent area of contact does not significantly affect the magnitude of friction; the dominant factors are the nature of the surfaces (through \$\mu\$) and the normal reaction \$R\$.