Profile
Settings
Refer your friends
Sign out
Dimensional Formula: The dimensional formula of any bodily amount is defined as the expression that represents how and which of the bottom portions are protected in that amount. It is denoted through enclosing the symbols for base portions with suitable strength in rectangular brackets, i.e. [ ] An example is the Dimension Formula of Mass, given as [M].
Friction is the resisting force between two surfaces, either in motion or trying to be in a state of motion. The coefficient of friction is denoted by a Greek sign (μ)
Coefficient of static friction
The coefficient of friction is the intrinsic property of the material, i.e., it depends only on the nature of the material. A smooth surface will have less coefficient of friction, and a rough surface will have more coefficient of friction. On a molecular level, it happens because of the uneven arrangement of molecules on the surface of the material.
The force of static friction is the product of normal force and coefficient of static friction. It can be written as,
Fs = μsN
where,
Fs -the maximum value of static friction force
μs -Coefficient of static friction,
N – Normal force,
- When the normal force N is lesser than the static frictional force Fs, N < Fs, the object is at rest, and we call it a static equilibrium condition.
- When the normal force N is equal to the static frictional force Fs, N = Fs, the object is in limiting equilibrium.
- When the normal force N is greater than the static frictional force Fs, N > Fs, the object is in motion, and so Fs becomes Fk, the kinetic friction.
Dimensional Formula of Coefficient of Friction
The coefficient of static friction is a scalar quantity. It does not have any unit or dimensions. The coefficient of static friction usually ranges between 0 and 1. There is no friction between the two objects if it is close to zero. On the other hand, if it is close to one, the friction between the objects equals the normal force. Sometimes, the coefficient is more significant when the frictional force is stronger than the normal force.
Derivation Of Dimensional Formula of Coefficient of Friction
Since the coefficient of friction is the ratio between frictional force and the normal force acting between them, it is a dimensionless quantity, i.e., (μ) = f/N
f = frictional force;
N = Normal force
Dimensional formula of frictional force = MLT-2
Similarly, Dimensional formula of Normal force = MLT-2
Thus, [μ] = MLT-2/MLT-2 =1.
The above derivation proves that the coefficient of friction is a dimensionless quantity.
It can seem like friction is just a force that dissipates energy, but the other side of the coin is that it helps us in various ways, e.g., it enables us to walk freely, helps us to stop moving vehicles, etc. One of the most important advantages of friction is that we can write on paper because of friction.
Coefficient of Rolling Friction
It is the ratio of the force of rolling friction to the weight of the object rolling.
μr = Fr / W …………. (N = W)
𝜇𝑠 is the static friction coefficient, 𝜇𝑘 is the kinetic friction coefficient, and 𝜇r is the coefficient of rolling friction.
𝜇𝑠 > 𝜇𝑘 >𝜇r
Conclusion
Coefficient of friction is basically the ratio of force acting between two objects to the force pushing them together. It is an internal property of material and happens due to irregular arrangement of molecules on the surface of the body. It is a dimensionless quantity and represented by (μ).
