A stationary object explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energy is what???
February 20th, 2023
I found that depends on the ratio of the two masses only.
I tried considerng ##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 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##