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
Apr 17, 2016

Answer:

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

Explanation:

enter image source here
#"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)#