Explain mathematical formulation of second law of motion
Answers
here is the proof;-
it is nothing but the formulation of the formula for the force.
according to Newton second law rate of change of momentum is proportional to the unbalanced force applied
first of all, momentum = m×v
change of momentum = mv - mu
= m(v-u)
the rate of change of momentum = m(v-u)÷t
now according to the Newton's law
m(v-u)÷t is proportional to F
now v-u/t = a
ma is proportional to f
F= kma
put the value of k be 1
we have F= Ma
hence proved, hope you will like my answer.
Answer:
we all know force=mass * acceleration
Explanation:
let the mass of moving object be 'm'
and the velocity of the objects changes from'u' to 'v' in the time interval 't'.
i.e,
initial velocity of the object=u
final velocity of the object is=v
total time interval=t
and momentum=a
we know,
momentum= mass * velocity
momentum of initial velocity = m*u=mu
momentum of final velocity= m*v= mv
change in momentum = mv-mu
rate of change of momentum = mv-mu/t
according to newton's second law of motion, the rate of change of momentum is directly proportional to the force applied.
i.e.,
force∝rate of change of momentum
⇒f∝mv-mu/t
⇒f∝m(v-u)/t
⇒f∝m*a (∵ v-u/t is referred to acceleration)
⇒f∝ma
⇒f = k*m*a (where k is the constant unit)
∵1 unit of force is defined as the mass of 1kg object produces an acceleration of 1m/s∧2
∴1 unit of force= k * 1kg*1m/s^2
⇒1 unit of force = 1*1kg*1m/s^2
=1kgm/s^2
hence, force = mass * acceleration