State Newton's second law of motion and derive its mathematical.
Answers
Answer:
Newton’s second law of motion can be formally stated as follows: 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.
Explanation:
Consider a body of mass m moving with initial velocity u. Let a force F acts on the body for time t so that the velocity of the body after time t is v.
Initial momentum = mu
Final momentum = mv
Now,
Change in momentum = mv - mu
= m(v-u)
Time taken to change this momentum = (t-0)
= t
Therefore,
Rate of change of momentum = Change in momentum/ Time taken
= m(v-u) / t
According to the definition of Newton's second law of motion,
Force applied is directly proportional to rate of change of momentum
Or, F is directly proportional to
m(v-u)/t.................(1)
Since v= u+at or (v-u/t) = a
Therefore, eqn. 1 can be written as
F is directly proportional to ma
Or, F= kma...........(2)
Where k is constant of proportionality
If F = 1 unit
m = 1 unit
And, a = 1 unit
Then from eqn (2),
1 = k or k= 1
Put this value of k = 1 in eqn 2, we get,
F= ma
Thus, force acting on the body is directly proportional to
- It's mass
- It's acceleration