Conservation of linear momentum

Conservation of linear momentum

According to principle of conservation of linear momentum in case of perfectly elastic collision both the linear momentum and kenetic energy of system conserved

imp---

if mass of balls are same than after the  collision it exchanges the velocity

Now let us suppose that the ball is moving toward a wall

P(initial)= (m*v)*i  ,  (i denote the motion in only x direction)

P(final)=  -(m*v)*i ,

So change in momentum of ball

=p(f) – p(i)   ,

=(-2mv)*i

Now let suppose there are ‘n’  no of molecules in the container having possible velocity

V1=(Vx1)i +(Vy1)j +(Vz1)k

V2=(Vx2)i +(Vy2)j +(Vz2)k

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Vn=(Vxn)i +(Vyn)j +(Vzn)k

Pressure on the wall due to x-component of velocity

For ball

 change in momentum of ball

=p(f) – p(i)   ,

=(-2mv)*i

For wall

change in momentum of ball

=p(f) – p(i)   ,

=(2mv)*i

 2l/v sec = time taken in 1 collision

I sec =v/2l collision

F= p*frequency

=2mv*v/2l

=mV2/l

F(x)= mv2/l(x1) + mv2/l(x2) + mv2/l(x3)…………..mv2/l(xn)

As

Pressure =force/area

=and area=L*L

Pressure in x direction= mV2/L +mv2/L + mv2/L+……………mv2/L

                                             1        +      2     +        3  +…………….     N

 Same as pressure in Y direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

      1        +      2     +        3  +…………….     N

And  Z-direction

= mV2/L +mv2/L + mv2/L+……………mv2/L

       1        +      2     +        3  +…………….     N

Now according to pascal law the pressure on any surface of container is always  same means by all component

So

Px = Py = Pz = P

Adding all the pressure

P + P +P =m(V2 + V2 + V2………..             V2)/L3

     

                       1       2   3                               n

3P = m(V2 + V2 + V2………..             V2)/L3

               1       2       3                           n

P= m(V2 + V2 + V2………..             V2)/3*L3

            1       2       3     .............  n

L3=V(volume of container)

P = = m(V2 + V2 + V2………..             V2)/3*V

               1       2       3                           n

This is nothing but maxwell’s theory of kenetic gases