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 $9 kg$ . What are the post-collision velocities of the balls?

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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 $9 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2016-04-17T15:09:36

$u_1=-24/7 m/s$
$u_2=60/7" "m/s$
$"TESTING"$
$color(green)(E_b=E_a)$

Explanation:

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$"using the equation (1)"$

$5*12+9*0=5*u_1+9*u_2$
$60+0=5*u_1+9*u_2$

$60=5*u_1+9*u_2" (a)"$

$"using the equation (3)"$

$12+u_1=0+u_2$

$u_2=12+u_1 " (b)"$

$"now use (a)"$

$60=5*u_1+9*(12+u_1)$

$60=5*u_1+108+9*u_1$

$60-108=14*u_1$

$-48=14*u_1$

$u_1=-48/14=-24/7 m/s$

$"finally ;use (b)"$

$u_2=12-24/7$

$u_2=(84-24)/7$

$u_2=60/7" "m/s$

$"testing"$

$"The Total Kinetic Energy before collision:"$
$E_b=1/2*5*12^2+0$

$E_b=72*5=360J$

$"The Total Kinetic Energy after collision:"$

$E_a=1/2*5*(-24/7)^2+1/2*9*(60/7)^2$

$E_a=(5*576)/(2*49)+(9*3600)/(2*49)$

$E_a=(2880+32400)/98$

$E_a=35280/98$

$E_a=360J$

$color(green)(E_b=E_a)$

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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 $9 kg$ . What are the post-collision velocities of the balls?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A ball with a mass of 5 kg 5 kg is rolling at 12 m/s12 m/s and elastically collides with a resting ball with a mass of 9 kg 9 kg. What are the post-collision velocities of the balls?

1 Answer

Explanation:

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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 $9 kg$ . What are the post-collision velocities of the balls?