Friction
What if Friction?
Friction is the opposing force that is set up between the surfaces of contact, when one body slides or rolls or tends to do so on the surface of another body.
According to Newton’s first law of motion, a body moving uniformly along a straight line would continue to do so unless an external force is applied on it. In practice, we find things otherwise. For example, a ball rolling over the floor stops after some time. Similarly, when we stop paddling our bicycle, it comes to rest after traveling a certain distance. Again, when we switch off the engine of our car, it stops after traveling some distance. All these examples show that there is some (invisible) force that opposes the motion of one body over the other. This opposing force is called Friction.
Again, when we apply a small force on a block, it does not move. The applied force must have been balanced by an opposing force (of friction). Thus, the force of friction comes into play even when one body tries to move over the surface of the other. Hence, we define friction as an opposing force that comes into play when one body actually moves (slides or rolls) or even tries to move over the surface of another body.
How sliding friction originates?
There are two theories for the cause of sliding friction.
- Old view
- Modern View
Old View
According to this view, the roughness of surfaces is the cause of friction. A surface which appears very smooth to the naked eye is found to have irregularities (roughness) when seen through a powerful microscope. This is true of every surface.
When two bodies are in contact with each other, the irregularities in the surface of one body get interlocked in the irregularities of the other surface. To move one body over the surface of the other, these interlockings have to be broken. Hence some force has to be applied. This applied force is a measure of friction between the two surfaces in contact. Obviously, the force of friction should be large when the area of contact is large. However, it is not true practically.
Modern View
The modern view of friction is that it arises on account of strong atomic or molecular forces of attraction between the two surfaces at the points of actual contact. On account of roughness of surfaces, the area of actual contact is much smaller than the area of apparent contact.
As force on the surface $=$ normal reaction $=$ weight of the body lying on it. This weight is constant. Therefore, pressure at the points of actual contact becomes very large. Due to this, molecules of the two surfaces at the points of actual contact come very close to one another and exert strong attractive molecular forces on one another.
These forces almost weld the surfaces and prevent relative motion between them. This is the cause of friction. According to the modern view, friction will be independent of the apparent area of contact. Further, when surfaces in contact are extra smooth, the force of adhesion between them will increase tremendously resulting in the increase of friction between them.
Frictional forces are classified as two types:
1. Internal friction
This type of friction occurs when there is a relative motion between the layers of any liquid. Its is also said as viscosity.
2. External friction
This type of friction arises when there are two bodies either trying to move or actually moving w.r.t each other. It is also called contact friction. External friction are of three types
- Static friction
- Limiting friction
- Kinetic friction
1. Static friction
The opposing force that comes into play when one body tends to move over the surface of another, but the actual motion has not yet started is called Static Friction.
Explanation
Let us consider a block of weight $mg$ lying on a horizontal surface as shown in figure. When a body presses against a surface, the surface deforms even if it appears to be rigid. The deformed surface pushes on the body with a normal force $R$ that is perpendicular to the surface. This is called normal reaction. It balances $mg$ i.e.
$ R=mg$
Suppose a small force $P$ is applied on the block to the right as shown. The force of friction $F$ opposes the motion. So long as the block does not move,
$F = P$
This means as we increase $P$, friction $F$ also increases, remaining equal to $P$ always.
As seen above, the magnitude of static friction is not constant. It always adjusts itself so as to be equal to the applied force.
2. Limiting friction
As we increase the applied force, a stage comes when the body is just at the verge of moving over the other. The static friction at this stage is obviously maximum. This maximum value of static friction is called Limiting Friction.
Hence, Limiting Friction is the maximum opposing force that comes into play when one body is just at the verge of moving over the surface of the other body.
3. Kinetic friction
When we increase the applied force slightly beyond limiting friction, the actual motion starts. This does not mean that friction has disappeared. It only means that the applied force is now greater than the force of limiting friction. The force of friction at this stage is called Kinetic Friction or Dynamic Friction.
Therefore, Kinetic Friction or Dynamic Friction is the opposing force that comes into play when one body is actually moving over the surface of another body.
It is found that the force of kinetic friction depends on normal reaction and on quality of finish of the rubbing surfaces. It does not depend upon the area of contact. But the kinetic friction does depend (though to a small degree) on the velocity of relative motion of the bodies.
If we plot a graph between the applied force and the force of friction, we get a curve of the type shown in figure. The part OA of the curve represents static friction, \( F_l \), which goes on increasing with the applied force.
At A, the static friction is maximum. This represents the limiting friction \( F_l = OL \). Beyond A, the force of friction is seen to decrease slightly. The portion BC of the curve, therefore, represents the kinetic friction \( F_k = OK \).
We have ignored here the dependence of kinetic friction \( F_k \) on the velocity of relative motion of the bodies.
Also, we find that kinetic friction is always slightly less than the limiting friction.
This is because, once the motion starts, actually, inertia of rest has been overcome. Also, when motion has actually started, irregularities of one surface have little time to get locked again into the irregularities of the other surface.
Further, dynamic friction or kinetic friction may be of two types:
1. Sliding friction
The opposing force that comes into play when one body is actually sliding over the surface of the other body is called sliding friction. For example, when a flat block is moved over the flat surface of a table, the opposing force is sliding friction.
2. Rolling friction
The opposing force that comes into play when one body is actually rolling over the surface of the other body is called rolling friction. For example, when a wheel, a circular disc or a ring or a sphere or a cylinder rolls over a surface, the force that opposes it is the rolling friction.
Cause of Rolling Friction
When a body rolls on a level track, the area of contact is very small. Therefore, the pressure exerted, which is equal to weight/area, is very large. This causes a depression in the surface below and a mount or bump in front as shown in the figure.
In turn, the surface of the rolling body in contact gets slightly compressed. Thus, a rolling wheel (i) constantly pulls out of depression and goes uphill on the mount LM, (ii) simultaneously detaches itself from the road KL, which is opposed by the forces of adhesion between the surfaces in contact. This causes rolling friction.
When a tyre is properly inflated, it becomes hard and gets compressed by the road to a much smaller extent. Therefore, rolling friction reduces. Hence it is easier to drive a bicycle when its tyres are fully inflated.
Note that the velocity of the point of contact of the wheel with respect to the floor remains zero all the time, although the center of the wheel moves forward. Therefore, rolling friction is often quite small compared to the sliding friction. That is why heavy loads are transported by placing them on carts with wheels. Thus sliding friction is converted into rolling friction. For example, rolling friction of steel on steel is hardly 1% of sliding friction of steel on steel.
Laws of Limiting Friction
The limiting friction obeys the following laws, which are based on experimental observations only:
1. The value of the limiting friction depends upon the nature of the two surfaces in contact and their state of roughness.
2. The force of friction is tangential (parallel) to the two surfaces in contact and acts opposite to the direction in which the body would start moving.
3. The value of limiting friction between two given surfaces is directly proportional to the normal reaction between the two surfaces.
Consider a body lying on a horizontal surface. If \( R \) is the normal reaction and \( F \) is the limiting friction (the value of applied force when the body just begins to slide), then
\[
F \propto R
\]
\[
F = \mu R
\]
i.e. $ \displaystyle \mu =\dfrac{F}{R}$
$ \displaystyle \text{(limiting friction)}\div \text{(normal reaction)}$
The constant of proportionality \( \mu \) is known as the coefficient of limiting friction.
Therefore, coefficient of limiting friction is defined as the ratio of the limiting friction to the normal reaction.
4. The value of limiting friction for any two given surfaces is independent of the shape or area of the surfaces in contact so long as the normal reaction remains the same.The laws of limiting friction are also applicable to the kinetic friction. As the kinetic friction is quite smaller than limiting friction, the coefficient of kinetic friction given by
$ \displaystyle {{\mu }_{k}}=\frac{{{{F}_{k}}}}{R}\quad $
i.e. $ \displaystyle {{\mu }_{k}}=\frac{{\text{kinetic friction}}}{{\text{normal reaction}}}$
is also much smaller than the coefficient of limiting friction.
Example:
A horizontal force of 490 N is required to slide a sledge weighing 600 kgf over a flat surface. Calculate the coefficient of friction.
Solution:
$ \displaystyle \begin{array}{l}F=490\text{N},\\R=Mg=600\text{kgf}=600\times 9.8\text{N}\end{array}$
Now,
\[
\mu = \frac{F}{R} = \frac{490}{600 \times 9.8} = 0.083
\]
