# Newtons second law of motion express it mathematically and find SI unit of force from it

2
by youaregoli

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by youaregoli

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force proportional to rate of change in motion

i.e.

F proportional to mv-mu/t

F=km(v-u)/t

here k is constant

so,

F=m(v-u)/t

and v-u/t =a (acceleration)

so,F=ma

Si unit is N or kgm/s²

consider a body of mass 'm' moving with certain velocity 'u' in a certain direction.If a force 'F' is applied on it in the same direction ,it's velocity increases.

After a small interval of time't' and it's velocity will be 'v'.

initial momentum of the body = mass * initial velocity = m*u

final momentum of the body = mass * final velocity = m*v

The momentum changes from 'mu to mv' in a time interval of 't'

According to NEWTON'S SECOND LAW OF MOTION , the rate of charge of momentum of a body is directly proportional to the applied force.

hence, F∞mv-mu÷t = F∞m(v-u)÷t

but v-u÷t = a (acceleration)

∴F∞ma

F=K ma (where k is constant)

if the value of K is taken as unity then,

∴F = ma

C.G.S. SYSTEM-----> gcm/s.sq = 1 dyne

S.I. SYSTEM----------->kgm/s.sq = 1 newton