A ball with a mass of # 5 kg# is rolling at #12 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

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Answer 1 · 2017-11-23T13:18:47

The velocities are #4/3ms^-1# and #40/3ms^-1#

Here it's an elastic collision with no loss of kinetic energy.

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

#m_1=5 kg#

#u_1=12 ms^(-1)#

#m_2=4 kg#

#u_2=0#

#v_1=?#

#v_2=?#

#5*12+4*0=5*v_1+4*v_2#

#5v_1+4v_2=60#............#(1)#

There is also conservation of kinetic energies

#1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2#

#5*12^2+4*0=5*v_1^2+4*v_2^2#

#5v_1^2+4v_2^2=720#.........#(2)#

From #(1)#, we get

#v_1=(60-4v_2)/5#

Plugging this value in #(2)#

#5*((60-4v_2)/5)^2+4v_2^2=720#

#((60-4v_2))^2/5+4v_2^2=720#

#16(15-v_2)^2+20v_2^2=720*5=3600#

#4(15-v_2)^2+5v_2^2=900#

#4(225-30v_2+v^2)+5v_2^2=900#

#900-120v_2+4v_2^2+5v_2^2=900#

#9v_2^2-120v_2=0#

#v_2(9v_2-120)=0#

#v_2=0# or #v_2=120/9=40/3=13.3ms^-1#

#v_1=(60-4*40/3)/5=4/3ms^-1#