Question

How many types of friction are there? Write their laws.

Answer 1

Explanation of Newton’s Second Law

According to Newton’s second law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force on the body, and this change takes place always in the direction of the applied force.
Let, m = mass of a body
v = velocity of the body
The linear momentum of the body
\(\vec{p}=m \vec{v}\) ………… (1)
let \(\vec{F}\) = External force applied on the body in the direction of motion of the body. .
\(\Delta \vec{p}\) = a small change in linear momentum of the body in a small time Δt.

Rate of change of linear momentum of the body = \(\frac{\Delta \vec{p}}{\Delta t}\)
According to Newton’s second law

Where k is proportionality constant. Taking the limit Δt → 0, the term \(\frac{\Delta \vec{p}}{\Delta t}\) becomes the
derivative or differential coefficient of \(\vec{p}\) w.r.t. time t.
It is denoted by \(\frac{d \vec{p}}{d t}\)
\(\vec{F}=k \frac{d \vec{p}}{d t}\)
Where k = 1 in all the system

As acceleration is a vector quantity and mass is scalar, therefore force \(\vec{F}\) being the product of m and \(\vec{a}\) is a vector. The direction of \(\vec{F}\) is the same as the direction of \(\vec{a}\). Equation (4) represents the equation of motion of the body. We can rewrite equation (6) in scalar form as :
F = ma …………. (7)
Thus, magnitude of force can be calculated by multiplying mass of the body and the acceleration produced in it. Hence, second law of motion gives a measure of force.
Dimension and Unit of Force :
As F = ma
∴ F= [M¹] [L¹T^-2 ] = [M¹L¹T^-2 ]
This is the dimensional formula of force.
Unit of force
The unit of force is Newton in (M.K.S.) system and dyne in C.G.S. system and Poundal in (F.P.S.) system.
Definition of 1 Newton
F = ma
When m = 1kg and a = 1 m/s^-2
then F = 1 Newton
The force which produces the acceleration of 1m/s^-2 in the 1 kg body, is equal to the 1 Newton.
1 Newton = 1 kg m/ s²
In C.G.S. System F = ma
If m = 1 g and a = 1 cm/s²
then F = 1 dyne

Thus 1 dyne is that force which produces 1 cm/s² acceleration in the mass of 1g body.