A ball with a mass of #2 kg# is rolling at #3 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 11, 2018

Answer:

Speed of moving ball after collision #"= 1 m/s"# (in the direction opposite to it’s initial direction of motion)
Speed of resting ball after collision #"= 2 m/s"#

Explanation:

Apply conservation of linear momentum

#"Initial total momentum = Final total momentum"#

#m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2#

#(2 × 3) + (4 × 0) = 2v_1 + 4v_2#

#6 = 2v_1 + 4v_2#

Didvide both sides by #2#

#3 = v_1 + 2v_2 color(white)(xxxxxxxxxxxxxxxx)(1)#

Now, use formula of coefficient of restitution (#e#)

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

For an elastic collision #e = 1#

#1 = (v_2 - v_1) / (3 - 0)#

#v_2 - v_1 = 3 color(white)(xxxxxxxxxxxxxxxxx)(2)#

Add equations #"(1) & (2)"#

#3 + 3 = v_1 + 2v_2 + v_2 - v_1#

#6 = 3v_2#

#color(blue)(v_2 = "2 m/s")#

Substitute #v_2 = "2 m/s"# in equation #(1)#

#3 = v_1 + (2 × "2 m/s")#

#color(blue)(v_1 = -"1 m/s")#