derive the mathematical expression of force
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Newton's second law states that the net force applied on the body is equal to the rate of change in its momentum. That is, when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t.
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p1 = mu
p2=mv
p2-p1=mv-mu=m(v-u)
We know that the rate of change of momentum with respect to time is proportional to the applied force. The applied force
F is directly propotional to m(v-u)/t
Or
F is directly propotional to m*a
Since a=v-u/t
F=k*m*a
Here, k is a proportionality constant. Thus, for simplycity k is defined as 1
Taking k=1
F=ma
p2=mv
p2-p1=mv-mu=m(v-u)
We know that the rate of change of momentum with respect to time is proportional to the applied force. The applied force
F is directly propotional to m(v-u)/t
Or
F is directly propotional to m*a
Since a=v-u/t
F=k*m*a
Here, k is a proportionality constant. Thus, for simplycity k is defined as 1
Taking k=1
F=ma
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