Question #83c7e

1 Answer
Oct 14, 2015

Answer:

I found that depends on the ratio of the two masses only.

Explanation:

I tried considerng Conservation of Momentum #p# (along #x#):
Before: #0#
After: #m_1v_1+m_2v_2#
and together:
#0=m_1v_1+m_2v_2#

so: #m_1v_1=-m_2v_2#

squaring both and rearranging:

#v_1^2/v_2^2=m_2^2/m_1^2#

Kinetic Energy is #K=1/2mv^2#
So:
#K_1/K_2=(cancel(1/2)m_1v_1^2)/(cancel(1/2)m_2v_2^2)#,
substituting: #v_1^2/v_2^2=m_2^2/m_1^2#
#K_1/K_2=(cancel(m_1))/(cancel(m_2))*m_2^cancel(2)/m_1^cancel(2)=m_2/m_1#