Question

write the mathmatical derivation of Newton's second law of motion.​

Answer 1

Answer:

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Explanation:

In equation form, Newton's second law of motion is a=Fnetm a = F net m . This is often written in the more familiar form: Fnet = ma. The weight w of an object is defined as the force of gravity acting on an object of mass m.

Answer 2

Answer:

Derivation of Newton's Second Law of Motion

Explanation:

Consider an object of mass m moving along a straight line with an initial velocity u (say). It is uniformly accelerated to velocity u in time t by the application of a constant force F in time t.

Then the initial momentum of the object = mu

P1 = mu

Final momentum of the object = mv

P2 = mv

Therefore change in momentum = mv-mu = m(v-u)

The rate of change in momentum = m×(v-u)/t

According to Newton's Second Law of Motion we have ,

F is proportional to m(v-u)/t

F = km (v-u)/t

F= k.m.a.......(1)

Here, a = (v-u)/t = the rate of change of velocity

= acceleration

k= a constant of proportionality

Putting m = 1 kg, a= 1ms^-2

F becomes 1 N.

So,

1 N = k×1kg×1ms^-2

therefore k = 1

From equation 1 we have ,

F = ma

This represents the second law of Motion

Thus, the second law of motion gives a method to measure the force acting on an object as a product of its mass and acceleration.

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