state and proof newtons 2nd law of motion
Answers
The rate of change in momentum is directly proportional to the applied force and take the direction in which direction force is applied .
According to the NSLM
for instantaneous change in velocity
dP/dt ∝ F
F ∝ dP/dt
but P = MV
F ∝ d(MV)/dt
F ∝ MdV/dt + VdM/dt
F = k(MdV/dt + VdM/dt )
F = 1(MdV/dt + VdM/dt )
F = MdV/dt + VdM/dt
if mass of the object is constant .
F = MdV/dt
dv/dt = a
F = Ma
Explanation:
Newton’s second law of motion can be stated as the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.Here we see that, the initial momentum
p1 = m × u
the final momentum
p2 = m × v
The change in momentum is
p2 – p1 = (m × v) – (m × u)
p2 – p1 = m (v – u)
The rate of change of momentum with respect to time is proportional to the applied force. The applied force is
F ∝ m (v – u)/t
or
F ∝ m × a
a = Rate of change of velocity/Time
F = k × m × a
k = proportionality constant.
Hence from the second law of motion, we get force is the product of mass and acceleration i.e F = ma.