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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