Question

State Newton's second law of motion. Also derive the mathematical relation for

Newton's second law of motion.

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Answer 1

When a force acts on a body, it changes the momentum of the body. Greater the force, greater will be the change in the momentum of the body. According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the net force acting on it and takes place in the direction of the net force.

Consider a body of mass m moving with some initial velocity u. If an unbalanced constant force is applied and it changes its velocity from u to v in time t, then the acceleration produced in the body is a.

The initial linear momentum of the body is pi = mu and final linear momentum is pf = mv.

The change in linear momentum = pf - pi = mv - mu = m (v - u)

or the rate of change of momentum = m( v - u ) / t

according to the Newton's second law that applied unbalanced force,

F proportional to m(v-u)/t

F proportional to m × a

or, F = k m a, where, K is the constant of proportionality

The unit of force is so chosen that the value of k is equal to 1. It is chosen as the amount of force exerted on a mass of 1 kg that produces in it an acceleration of 1ms^-2.

Therefore, F = ma

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Answer 2

Answer:

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