delivation of second law of motion ..
Answers
hello!
Newton’s Second Law -
Newtons Second Law of motion states that, the rate of change in momentum is directly proportional to the force applied and the object moves in the direction of force applied.
F ∝ dp / dt
where f = force
dp = change in momentum
dt = change in time
F ∝ dp/dt [Greater the change in momentum, greater is force]
F = k dp/dt
F = dp/ dt
F = d/ dt (mv)
Let, m: mass of the body be constant
F = m dv/dt
F = ma
Newton’s Second law is consistent with the First law
F = ma
If F =0, then a = 0
According to First law, if a = 0, Then F = 0
Thus, both the laws are in sync.
Vector form of Newton’s Second law
Fx = dpx/ dt = max
Fy = dpy/ dt = may
Fz = dpz/dt = maz
Newton’s Second Law was defined for point objects. For larger bodies,
a: acceleration of the centre of mass of the system.
F: total external force on the system.
Hello friend
Here is your answer
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The second law of motion states that
The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.
As we know,
Change of momentum = P2 - P1
Where P2 = mv and P1 = mu
Thus,
Change of momentum = mv - mu
And
Rate of change of momentum = mv - mu/t
Or the applied force,
F is proportional to m(v-u)/t
F = km(v-u)/t
F = kma
As we know that v - u /t = a
Thus, F =kma where k is a constant proportion
.
Thus F = ma
Hope it helps !