A ball with a mass of #3 kg# moving at #4 m/s# hits a still ball with a mass of #9 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

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Answer 1 · 2016-08-12T06:19:25

#"The lost kinetic energy of system will be -16 J."#

#"First ,let us find the velocity of second ball for after collision"#

#"Use the conversation of momentum"#

#m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'#

#"where;"#

#m_1=3" "kg#
#v_1=4" "m/s#
#m_2=9" "kg#
#v_2=0#
#v_1^'=0#
#v_2^'=?#

#3*4+9*0=3*0+9*v_2^'#

#12+0=0+9*v_2^'#

#12=9v_2^'#

#v_2^'=12/9=4/3" "m/s#

#"Total kinetic energy before collision:"#

#E_B=1/2*m_1*v_1^2+1/2*m_2*v_2^2=1/2(m1*v_1^2+m_2*v_2^2)#

#E_B=1/2(3*4^2+9*0)#

#E_B=1/2(3*16)=24J#

#"Total kinetic energy after collision:"#

#E_A=1/2*m_1*(v_1^')^2+1/2*m_2*(v_2^')^2#

#E_A=0+1/2*9*(4/3)^2#

#E_A=1/2*cancel(9)*16/cancel(9)#

#E_A=8J#

#"The lost kinetic energy:"#

#E_L=E_A-E_B=8-24=-16J#