A ball with a mass of $5 kg$ is rolling at $6 m/s$ and elastically collides with a resting ball with a mass of $3 kg$ . What are the post-collision velocities of the balls?

Question

1631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-17T12:38:32

$color(red)(v_1^'=3/2 m/s)$
$color(red)(v_2^'=15/2)$

$"momentums before collision"$
$P_1=m_2*v_1=5*6=30" " kg*m/s$
$P_2=m_2*v_2=3*0=0$
$Sigma vec P_b=vecP_1+vec P_2" total momentum before collision"$

$Sigma vec P_b=30+0=30 " "kg*m/s$

$"total momentum after collision must be "30 " "kg.m/s$

$"momentums after collision"$
$vec P_1^'=m_1*v_1^'=5*v_1^'$
$vec P_2^'=m_2*v_2^'=3*v_2^'$

$Sigma P_a=vec P_1^'+vec P_2^'$
$Sigma P_a=5*v_1^'+3*v_2^'$

$Sigma vec P_b=Sigma vec P_a$

$30=5*v_1^'+3*v_2^'" "(1)"$

$v_1+v_1^'=v_2+v_2^'$
$6+v_1^'=0+v_2^'$
$v_2^'=6+v_1^'" (2)"$

$"use the equation (1)"$

$30=5v_1^'+3(6+v_1^')$
$30=5v_1^'+18+3v_1^'$
$30-18=8v_1^'$
$12=8v_1^2$
$v_1^'=12/8$
$color(red)(v_1^'=3/2 m/s)$

$"use (2)"$
$v_2^'=6+v_1^'$
$v_2^'=6+1,5$

$color(red)(v_2^'=15/2)$

A ball with a mass of 5 kg 5 kg is rolling at 6 m/s6 m/s and elastically collides with a resting ball with a mass of 3 kg3 kg. What are the post-collision velocities of the balls?