We know that F = m × a. How did they derive this. Today let us see how to derive this formula.
F = ma ? How ?
Momentum:
It is described as
p = m × v
This says that momentum is directly proportional to mass and velocity.
SI unit: Kg m/s
We also know that change in momentum is written as:
p₂ − p₁
mv - mu
where, m denotes mass and v denotes final velocity and u denotes initial velocity
We know that Newton's second law of motion is:
The rate of change of of momentum is directly proportional to the force applied on the object.
So, mathematically, it is
F ∝ change in momentum / Time taken
F ∝ p₂ − p₁ / t
F ∝ (mv - mu) / t
F ∝ m( v − u) / t
F ∝ m × ( v − u) / t
We know that a = ( v − u) / t
So substitute,
F ∝ m × a
To remove the proportionality sign multiply the constant - k
F = k × m × a ; k = 1
F = ma
To remove the proportionality sign multiply the constant - k
F = k × m × a ; k = 1
F = ma
We derived the equation: F = m × a
