Newton’s second law of motion states that the force exerted by a body is directly proportional to the rate of change of its momentum. For a body of mass ‘m’, whose velocity changes from u to v in time t, when force ‘F’ is applied.
F∝
Time
Changeinmomentum
F∝
t
mv−mu
F∝m(
t
v−u
)
⇒F∝ma⇒F=kma(∵a=
t
v−u
)
⇒F=ma(∵k=constant=1)
Answers
Answer:
Answer:
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.