Huge collision!

Classical Mechanics Level 2

Three balls having masses $2m$ , $3m$ and $5m$ having equal velocities $v_0$ collide with a block of wood of mass $6m$ which is at rest, in a perfectly elastic collision.

Now, this whole system of the balls and the block is moving with a velocity of $v_1$ .

If the ratio $\dfrac{v_0}{v_1}$ is equal to $\dfrac ab$ , where $a$ and $b$ are co-prime, find $a+b$ .

The answer is 13.

1 solution

Sravanth C.
Jan 22, 2016

From conservation of momentum we know that sum of initial momenta of all objects before collision is equal to the sum of their final momenta.

Here, the sum initial momenta of the balls and the block is equal to: $2mv_0+3mv_0+5mv_0+6m(0)=15mv_0$ .

But, after collision the balls and the block become a single system, hence the final momentum of the whole system will be: $(2m+3m+5m+6m)v_1=16v_1$ . And now we have, $\sum p_i=\sum p_f\\10mv_0=16mv_1\implies\boxed{\dfrac{v_0}{v_1}=\dfrac{16}{10}=\dfrac 85}$

Therefore, $a=8$ and $b=5$ , so $a+b = 13$ .

Huge collision!

The answer is 13.

1 solution

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