A ball with a mass of 3 kg is rolling at 16 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
Jun 29, 2016

v_r^'=-7.27" "m/s" The red ball's velocity after collision"
v_b^'=8.73" "m/s" The blue ball's velocity after collision"

Explanation:

enter image source here

"BEFORE COLLISION"

m_r=3" kg The red ball's mass"
v_r=16" "m/s " The velocity of red ball before collision"

P_r=m_r*v_r=16*3=48 kg*m/s
P_r:"(The red ball's momentum before collision)"

m_b=8" kg The blue ball's mass"
v_r=0" "m/s " The velocity of blue ball before collision"

P_b=m_b*v_b=8*0=0
P_b=0

P=P_r+P_b=48+0=48 kg*m/s

P:"(The Total momentum before collision)"

"AFTER COLLISION"

P_r^'=3*v_r^'" The red ball's momentum after collision"
P_b^'=8*v_b^' " The blue ball's momentum after collision"
P_^'=P_r^'+P_b^'
P^'=3*v_r^'+8*v_b^'

P^':"The total momentum after collision"

P=P^'" The conservation of momentum"

48=3*v_r^'+8*v_b^' " equation 1"

v_r+v_r^'=v_b+v_b^'" equation 2"
16+v_r^'=0+v_b^'
v_b^'=16+v_r^'" plug in equation 1"

48=3*v_r^'+8*(16+v_r^')

48=3v_r^'+128+8v_r^'

11v_r^'=48-128

11 v_r^'=-80

v_r^'=-80/11

v_r^'=-7.27" "m/s" The red ball's velocity after collision"

"So;"
v_b^'=16+v_r^'

v_b^'=16-7.27

v_b^'=8.73" "m/s" The blue ball's velocity after collision"