Newton second law of motion derivation
Answers
Answer:
Let 'm' = mass
'u' = initial speed
'v' = final speed
't' = time interval and
'F' = force.
~ is directly proportional.
Derivation:
Initial momentum of body = mu
Final momentum of body = mv
change in momentum ∆p = mu - mv
By newton's second law of motion,
Force, F ~ rate of change in momentum.
F ~ change in momentum / time.
F ~ mv - mu / t
F = km(v-u) / t
Here, k is constant k = 1.
F = m(v-u) / t
since, acceleration a= (v-u) / t.
F = m * a
Force = mass * acceleration.
Newton's 2nd law of motion states that ;
" The rate of change of momentum is directly proportional to the unbalance force in the direction of force "
Consider a body of Mass m having an initial velocity u. The initial momentum of this body will be mu. Suppose a force F acts on this body for time t & causes the final velocity to become v. The final momentum of this body will be mv. Now,the change in momentum of this body is mv - mu & the time taken for this change is t. So, According to Newton's First Law of Motion :
Recall the first equation of motion
v = u + at
Substitute this value in above one
Hence,
But we need to remove the proportionality symbol ,
In order to remove it we need to add an proportionality constant.
So,
k = 1
So,
Derived.