A ball with a mass of # 3 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of # 8 kg#. What are the post-collision velocities of the balls?

1 Answer
Apr 7, 2018

Answer:

#-"2.72 m/s"# and #"3.27 m/s"#

Explanation:

From conservation of momentum

#"Initial total momentum = Final total momentum"#

#m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2#

#("3 kg × 6 m/s") + ("8 kg × 0 m/s") = ("3 kg" × v_1) + ("8 kg" × v_2)#

#18 = 3v_1 + 8v_2 color(white)(...)……(1)#

Coefficient of restitution #(e)# is given by

#e = (v_2 - v_1) / (u_1 - u_2)#

For perfectly elastic collision #e = 1#

#1 = (v_2 - v_1)/ (6 - 0)#

#v _2 - v_1 = 6#

Multiply both sides by #3#

#3v_2 - 3v_1 = 18 color(white)(...) ……(2)#

Add equations #(1)# and #(2)#

#18 + 18 = 3v_1 + 8v_2 + 3v_2 - 3v_1#

#36 = 11v_2#

#v_2 = 36/11 = color(blue)"3.27 m/s"#

Substitute #v_2 = 3.27# in equation #(1)#

#18 = 3v_1 + (8 × 3.27)#

#v_1 = (18 - (8 × 3.27))/3 = color(blue)(-"2.72 m/s")#