Question

Express Newton's second law of motion mathematically explaining the symbols used ​

Answer 1

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$\huge\bold\purple{Answer:-}$

⏩ Measurement of force from Newton's second law:-

Suppose a force F acts on a body mass m and changes it's velocity from u to v in t seconds. Then,

➡ Initial momentum of the body, P1= mu

➡ Final momentum of the body, P2= mv

Change in momentum= P2- P1 = mv-mu = m(v-u)

Time taken = t

Therefore,

Rate of change of momentum= Change in momentum/ time taken

= Final momentum- Initial momentum/ Time taken

= mv- mu/t

= m(v-u)/t

= ma (Since v-u/t= a)

where a is the acceleration of the body.

Now, in accordance to Newton's second law, the rate of change of momentum is directly proportional to the applied force, so,

$</em><em>F</em><em>\alpha \: ma$

or F= kma

where k is a constant. The unit of force is so chosen that k is equal to one. If m= 1, a=1 and F= 1, then

1= k. 1. 1 or k= 1

Therefore,

F= ma or Force= Mass × Acceleration.

→So, a unit force is that force which produces a unit acceleration in a body of unit mass.

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Answer 2

Explanation:

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