A ball with a mass of 5 kg is rolling at 7 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

1 Answer
Gió
Jan 6, 2016

I found: 0.78 and 7.78 m/s but check my maths!

Explanation:

We can use conservation of momentum vecp=mvecv in one dimension (along x). So we get:

p_("before")=p_("after")

So:

(5*7)+(4*0)=(5*v_1)+(4*v_2)

Being an elastic collision also kinetic energy K=1/2mv^2 is conserved:

K_("before")=K_("after")

So:
1/2*5*7^2+1/2*4*0^2=1/2*5*v_1^2+1/2*4*v_2^2

We can use the two equations together and we get:

{(35=5v_1+4v_2),(245=5v_1^2+4v_2^2):}

From the first equation:
v_1=(35-4v_2)/5
Substitute into the second and get:
245=cancel(5)(35-4v_2)^2/cancel(25)^5+4v_2^2
cancel(1225)=cancel(1225)-280v_2+16v_2^2+20v_2^2
36v_2^2-280v_2=0
v_2=0m/s (not) and v_2=280/36=70/9=7.78m/s yes.
Corresponding to:
v_1=7m/s and v_1=7/9=0.78m/s

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