Question

A sphere of mass 12kg and another one of mass 8 kg are moving towards each other in a smooth linear groove. The speed of the heavier sphere is 3 times that of the lighter sphere . After collision the heavier sphere has a speed of 4/1/6 m/s and the lighter sphere a speed of 6m/s . Calculate the speeds of the sphere before collisions

Answer 1

Solution.

$m_1=12kg;$

$m_2=8kg;$

$v_{01}=3v;$

$v_{02}=v;$

$v_1=4\dfrac{1}{6}m/s;$

$v_2=6m/s;$

$m_1\overrightarrow{v_{01}}+m_2\overrightarrow{v_{02}}=m_1\overrightarrow{v_{1}}+m_2\overrightarrow{v_{2}};$

$m_1v_{01}-m_2v_{02}=m_1v_1+m_2v_2;$

$12\sdot3v-8v=12\sdot4\dfrac{1}{6}+8\sdot6;$

$36v-8v=50+48;$

$26v=98;$

$v=98/26;$

$v=3\dfrac{10}{13};$

$v_{01}=3\sdot3\dfrac{10}{13}=11\dfrac{4}{13}m/s;$

$v_{02}=3\dfrac{10}{13}m/s;$

Answer: $v_{01}=11\dfrac{4}{13}m/s;v_{02}=3\dfrac{10}{13}m/s.$