Physics, asked by ana205, 1 year ago

explain the ticked places.... ( mathematical representation of force and units of force ). explain the SI unit, CGS unit and relation between newton and dyne properly (step wize) with some examples of your own.... thanks

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Answered by skh2

Hello,

Force can be expressed mathematically with the help of newtons second law of motion
It states that :
The force applied on a body is directly proportional to the net change in the momentum and inversely proportional to the time taken for the change.
Now, it means that :-

F directly proportional to change in momentum that is final momentum - initial momentum

$force = \frac{change \: in \: momentum}{time \: taken}$
$force = \frac{mv - mu}{t} = \frac{m(v - u)}{t} = ma$
Since, acceleration is = v-u/t

Now,
Force contains mass and acceleration.
So, si unit of mass is kg and acceleration is m/sec²
So,
Si unit of force is kg m /sec²
In order to give honor to famous scientist Isaac Newton we write the si unit of force as Newton (N)

Now,
CGS unit is called as centimeter gram second
So,
1N = 1kg * 1 m/sec² = 1000 g * 100cm/sec²=10^5 dyne

Hope this will be helping you ✌️

skh2: similarly, 1 dyne is acceleration of 1 cm/sec² produced on body of mass 1 gram

skh2: that is like gram is smaller unit of weight. similarly, dyne is smaller unit of force

skh2: in the mathematical representation 1 thing is missing. it is that the force is directly proportional to mass*acceleration. so, to remove proportionality sign we need to multiply a constant. in case of force the constant is 'k'. its value is 1

skh2: i mean to say that F= k*m*a

skh2: suppose, 1 N force is applied on 1 kg body producing 1 m/sec² acceleration.

skh2: so, 1 = k *1*1

skh2: so, value of k becomes 1

skh2: hope this will be helping you ✌️

ana205: Thanks a lot :)

skh2: welcome

Answered by Itztomato

Refer to above attachment..

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