Question

how will you arrive at a mathematical formula to measure force using second law of motion define the unit of force using the formula

Answer 1

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system.

Force applied is directly proportional to the product of mass and acceleration .

Let $p_{i} , p_{f}$ be the initial and final momentums respectively.

According to newton's second law :-

pf - pi / t ∝ F

We know that,
Momentum ( P) = mv .

Let v be the final and u be the initial velocity .

Now,

mv - mu / t ∝ F

F ∝ m ( v-u) /t

F ∝ ma.

F = kma.

Here, K is the proportionality constant. It's value is 1 .

Units of Force are given by the units of mass and acceleration. Units of force is Kgm/s² .

In accordance to honour the contributions of Newton, 1 kgm/s² is termed as 1 Newton..

Definition of 1 Newton is the force required to move or displace a 1 kg body with 1m/s² acceleration.

Answer 2

Hey!


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According to Newton's second law of motion, rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.

DERIVATION FOR SECOND LAW OF MOTION

Let,

m= mass of the body
u= initial velocity of the body
v= final velocity of the body
t= time for which the force is applied
F = an external force applied on body

Initial momentum of the body, p1= mu
Final momentum of the body, p2= mv

Rate of change of linear momentum of the body,

p2-p1= mv-mu= m(v-u)/t

We know that, v-u/t= a
Rate of change of linear momentum= ma

According to Newton's second law of motion,
Rate of change of linear momentum ∝ force applied

Thus,

F∝ma
F=kma

k= constant
Unit force is that much force which produces unit acceleration Inna body of unit mass, thus,

F= kma
k=1
F= 1×1×1
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=> F= ma
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Unit of force= Newton, N
Onw Newton force is that much force which produces an acceleration of 1m/s^2 in a body of mass 1 kg.

Unit of force according to the formula,

When,
m= 1kg
a= 1m/s^2

F= ma
F= 1kg×1m/s^2
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F= 1 kg m/s^2

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Hope it helps...!!!