A ball with a mass of 5 kg is rolling at 2 m/s and elastically collides with a resting ball with a mass of 2 kg. What are the post-collision velocities of the balls?

1 Answer
ali ergin
Dec 16, 2016

"velocities of objects after collision are:"
"the red ball's velocity :"v_1^'=6/7" "m/s" at positive direction"
"the blue ball's velocity :"v_2^'=20/7 " "m/s" at positive direction"

Explanation:

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"let the velocities of objects after collision be "v_1' " and " v_2^'

P_1':" momentum of the red ball after collision"
v_1^':"velocity of the red ball after collision"

P_1^'=m_1*v_1^'
P_1^'=5*v_1^'

P_2^':"momentum of the blue ball after collision"
v_2^':"velocity of the blue ball after collision"

P_2^'=2*v_2^'

"vectorial sum of the momentums after collision :"
P_a=P_1^'+P_2^'
P_a=5v_1^'+2v_2^'

P_b=P_a" conservation of momentum"

10=5v_1^'+2v_2^'" "(1)

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"the total velocities of the objects must be equal"

v_1+v_1^'=v_2+v_2^'

2+v_1^'=0+v_2^'

color(red)(v_2^'=2+v_1^')" "(2)

"use (1)"

10=5v_1^'+2(color(red)(2+v_1^'))

10=5v_1^'+4+2v_1^'

10=7v_1^'+4

10-4=7v_1^'

6=7v_1^'

color(green)(v_1^'=6/7)" "m/s

"use (2)"

v_2^'=2+color(green)(6/7)

v_2^'=20/7" "m/s

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