# elastic collision and to find mass ratio of masses A and B

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A body A experiences perfectly elastic collision with stationary body B. if after collision the bodies fly apart in the opposite direction with equal speeds the mass ratio of a and b.

I applied conservation of linear momentum
$m_1u_1=m_2v-m_1v$ where v be there final velocity.
and then I used coservation of energy.
$m_1u_1^2 =v^2 (m_1+ m_2)$
but I am not able to take out the ratio

asked Nov 25, 2016

1 vote

Find $u_1/v$ from the 1st eqn and substitute into the 2nd :

From the 1st equation
$m_1u_1=(m_2-m_1)v$
$u_1/v=(m_2-m_1)/m_1=\mu-1$
where $\mu=m_2/m_1$ which must be $\ge 1$ because $u_1/v \ge 0$.

The 2nd equation can be written as
$(u_1/v)^2=(m_1+m_2)/m_1=1+\mu$ .
Substitute for $u_1/v$ :
$(\mu-1)^2=\mu^2-2\mu+1=1+\mu$
$\mu^2-3\mu=\mu(\mu-3)=0$.

Therefore $\mu=m_2/m_1=0$ or $3$. We must have $\mu \ge 1$ for realistic solutions so $m_2/m_1=3$ is the only solution.

answered Nov 25, 2016 by (27,556 points)
edited Nov 26, 2016
If you could elaborate a bit so it is more clear for future users, that'd be great!