Question

When an object of mass m moving with velocity v collides with an object of mass M moving with velocity V and sticks to it, then the law of conservation of momentum states that mv + MV = (m+M)u where u is the final velocity of the combined object. Solve this equation for m in terms of the other quantities. (This equation gives the recoil when you fire a gun.)

Answer 1

m = M (u-V)/(v-u)

Explanation:

We know that:

`mv + MV = (m+M)u = mu + Mu`

If we sum -mu to both sides of the equation we get:

`mv -mu +MV =Mu + (mu-mu)=Mu`

Now let's sum -MV to both sides:

`mv - mu = mv -mu + (MV-MV) = Mu -MV`

Now we can factor the m and M terms:

`m(v - u) = M(u - V)`

Finally we can divide by v-u ***

`m(v-u)/(v-u)=M(u-V)/(v-u)`

Since (v-u)/(v-u) =1

m = M (u-V)/(v-u)

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If u=v it will imply that V=u and tehrefore the two mases will travel with the same velocity to the same direction and no collision would take place

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