A ball with a mass of # 3 kg# is rolling at #1 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

1 Answer
Mar 9, 2016

Answer:

#v_1^'=-1/7 m/s#
#v_2^'=6/7m/s#

Explanation:

#m_1*v_1+m_2v_2=m_1v_1^'+m_2v_2^'" "(1)#
#"total momentum before collision=total momentum after collision"#
#1/2*m_1*v_1^2+1/2*m_2*v_2^2=1/2.m_1*v_1'^2+1/2*m_2*v_2'^2#

#m_1*v_1^2+m_2*v_2^2=m_1*v_1'^2+m_2*v_2'^2" "(2)#
#"we obtain the equation of (3),if we arrange (1) and (2)"#
#v_1+v_1^'=v_2+v_2^' " "(3)#
#3*1+4*0=3*v_1^'+4*v_2^'#
#3=3*v_1^'+4*v_2^'" "(4)#
#"use (3)"#
#1+v_1^'=0+v_2^'#
#v_2^'=1+v_1^'" "(5)#
#"use (4)"#
#3=3*v_1^'+4(1+v_1^')#
#3=3*v_1^'+4+4v_1^'#
#-1=7v_1^'" "v_1^'=-1/7 m/s#
#"use (5)"#
#v_2^'=1-1/7#
#v_2^'=6/7m/s#