Question

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=) How is the change in momentum related to force. Explain....!!


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Answer 1

if the mass and velocity of object will change the momentum will also change

Answer 2

Hey friend,

Here's your answer,



Change in momentum of a body per unit time is directly proportional to the unbalanced forced acting on the body and the change in momentum takes place in the direction of the unbalanced force acting on the body.


i.e.,         F is inversely proportional to dp / dt


where,


dp = change in momentum
dt = time taken for this change in momentum



RELATION BETWEEN MOMENTUM AND FORCE



Consider a body of mass m moving with initial velocity u. Let a Force F act on the body for time t so that the velocity of the body after time t is v.


Initial momentum of the body, pi = mu

Final momentum of the body, pf = mv

Now,

Change in momentum of the body = pf- pi

                              = mv - mu

                              = m(v-u)


Time taken to change this momentum = (t-0) = t

∴ Rate of change of momentum = Change in momentum / Time taken

= m (v - u) / t



According to the definition of Newton's second law of motion,


Force applied is inversely proportional to  rate of change of momentum

Or,

F = m( v-u) /t

Since,

v = u+at
 
or,


(v - u) /t = a


Therefore,

Eqn 1 becomes,

F is inversely proportional to ma

F = kma

Where,

k = constant

If,

F = 1 unit
m = 1 unit
a = 1 unit
k = 1

Therefore,


F = ma


Thus,

 F = ma

momentum = ma

∴ Force = Momentum

Hence,

Force is directly proportional to :-


Mass

and

Acceleration



Hence proved.



Hope this helps!!!