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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.)

Respuesta :

horaciocrotte

Answer:

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

Step-by-step explanation:

We know that:

[tex]mv + MV = (m+M)u = mu + Mu[/tex]

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

[tex]mv -mu +MV =Mu + (mu-mu)=Mu[/tex]

Now let's sum -MV  to both sides:

[tex]mv - mu = mv -mu + (MV-MV) = Mu -MV[/tex]

Now we can factor the m and M terms:

[tex]m(v - u) = M(u - V)[/tex]

Finally we can divide by v-u ***

[tex]m\frac{v-u}{v-u}=M\frac{u-V}{v-u}[/tex]

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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