# Friction force

1. Definition of the friction force

Friction is a drag that works between the surfaces of objects that touch each other. In this topic, the frictional force studied is related to the frictional force acting between two solid body surfaces that touch such as friction between the base of the beam and the floor surface, friction between the shoe base and the floor surface, friction between the wheels of the car and the road surface.

The friction force always works on the surface of solid objects that touch each other, even though the object is very smooth. Even smooth surfaces are actually very rough on a microscopic scale. When an object moves, these microscopic ridges interfere with the motion. At the atomic level, a protrusion on the surface causes atoms to be very close to other surfaces, so that the electric forces between atoms can form chemical bonds, as a union between two surfaces of a moving object. When an object moves, for example when you push a book on the surface of the table, the movement of the book experiences obstacles and finally stops. This is due to the formation and release of the bond.

If the surface of an object rubs against the surface of another object, each of these objects works on friction between one another. The friction force on the moving object is always in the opposite direction to the direction of movement of the object. In addition to inhibiting the motion of objects, friction can cause wear and damage. We can observe this on the vehicle engine. For example, when we provide lubricating oil on a motorcycle engine, we actually want to reduce the friction force that occurs inside the engine. If it is not given the lubricating oil, our vehicle engine is damaged quickly. This example is one of the losses caused by friction.

2. Types of friction forces

There are two types of frictional forces namely the force of static friction (fs) and the force of kinetic friction (fk). The static friction force works when the object has not moved while the kinetic frictional force works when the object is moving. If you push a table but the table hasn’t moved then the friction force acting on the table that is rest is a static friction force. Conversely, when the table is moving, the friction force acting on the table is kinetic friction. If the moving table is not always pushed, the table will stop after moving for a while. The table stops due to the kinetic friction force that blocks the movement of the table.

Ever slipped when stepping on something smooth? When you slip, the friction force that works between the base of the shoe or the bottom of a sandal with a smooth surface is kinetic friction. This problem is similar to when a motorcycle or car moves over a wet and smooth road surface braked until the wheel slips. When the wheels slip, the friction force acting on the surface of the wheel and the road surface is kinetic friction force. Conversely, when you walk, the friction force that works between the shoe base or the bottom of the sandals with the floor surface is a static friction force. Likewise, when the wheels do not slip, the friction force acting on the surface of the wheel and the road is static friction.

2.1 Static friction force

The static friction force is frictional forces acting on the surface of objects that touch each other when objects not yet moved.

Figure 1 shows an object that is still on the surface of a flat plane. If the object not yet moved then the static friction force (fs) is smaller than the pull force (F). If it continues to be pulled then the object will move. When the right object will move, the magnitude of the static friction force (fs) equals the magnitude of the pull force (F).

Newton’s First Law states that objects are rest if the total force (resultant force) is zero.

ΣFy = 0 (Object rest and do not move in a vertical direction)

N – w = 0

N = w (1.2)

Replace N in equation 1.1 with N in equation 1.2

fs = μs w

fs = μs m g (1.3)

fs = static friction (N), μs = coefficient of static friction, N = normal force (N), w = gravity (N), m = mass (kg), g = acceleration of gravity (m/s2)

If you want to determine the coefficient of static friction then use equation 1.1 b

Σfx = 0 (Object rest and not move in the horizontal direction)

F – fs = 0

F = fs (1.4)

When the object starts to move, the maximum static friction force equals the magnitude of the push or pull force.

2.2 Kinetic friction force

The kinetic friction force is the frictional force acting on the surface of objects that touch each other when an object is moving.

If you want to determine the coefficient of kinetic friction (μk), use equation 1.5 b

Figure 2 shows an object being pulled regularly so that the object moves at a constant speed. When moving at a constant speed, the magnitude of the kinetic friction force (fk) equals the magnitude of the pull force (F).

Newton’s First Law states that an object moves at a constant speed if the total force (resultant force) is zero.

ΣFx = 0 (objects move at a constant speed in the horizontal direction)

F – fk = 0

F = fk (1.6)

Sample problem 1:

A student pulls a beam with a mass of 1 kg which is located on the table surface using a dynamometer (a force measuring device). When the beam will move, the dynamometer shows the number 2 N. If the acceleration of gravity = 10 m/s2, determine (a) the magnitude of the static friction force (b) the coefficient of static friction

Solution:

Known: m = 1 kg, F = 2 N, g = 10 m/s2, w = m g = 10 N

(a) fs

When the beam will move, the magnitude of the static friction force = the magnitude of the pull force (compare equation 1.4). So fs = F = 2 N.

(b) μs

fs = μs w

2 N = (μs)(10 N)

μs = 2 N / 10 N = 0.2

Sample problem 2:

A beam with a mass of 1 kg located above the table surface is pulled regularly so that the beam moves at a constant speed. When the beam moves at a constant speed, the dynamometer shows the number 1 N. If the acceleration of gravity = 10 m/s2, determine (a) the magnitude of the kinetic friction force (b) the coefficient of kinetic friction

Solution:

Known: m = 1 kg, g = 10 m/s2, F = 1 N, w = m g = 10 N

(a) fk

When the beam moves regularly or moves at a constant speed, the magnitude of the kinetic friction force = the magnitude of the pull force (compare equation 1.6).

So fk = F = 1 N

(b) μk

fk = μk w

1 N = (μk)(10 N)

μk = 1 N / 10 N = 0.1