1. The problem statement, all variables and given/known data An object with total mass mtotal = 8.6 kg is sitting at rest when it explodes into two pieces. The two pieces, after the explosion, have masses of m and 3m. During the explosion, the pieces are given a total energy of E = 48.0 J. 1) What is the speed of the smaller piece after the collision? 2) What is the speed of the larger piece after the collision? 3) If the explosion lasted for a time t = 0.028 s, what was the average force on the larger piece? 4) What is the magnitude of the change in momentum of the smaller piece? 5) What is the magnitude of the velocity of the center of mass of the pieces after the collision? 2. Relevant equations Ek = P^2/2m Ek = 0.5*m*v^2 ΔP = Pf - Pi F = ΔP/Δt 3. The attempt at a solution m1 (smaller piece) should be 1/4 of mtotal, so m1=2.15 kg m2 (larger piece) should be 3/4 of mtotal, so m2=6.45 kg We're told the pieces are given a total of 48 J, I simply assumed that 1/4 of that energy goes to m1 and the other 3/4 to m2. This is probably where I am going wrong. From there I solved for velocity using Ek and mass: v1 = sqrt(2*Ek/m1) = sqrt(2*12/2.15) = 3.341 m/s Also tried assuming each piece was given a total of 48 J: v1 = sqrt(2*Ek/m1) = sqrt(2*48/2.15) = 6.682 m/s Also tried assuming each piece was given a total of 24 J: v1 = sqrt(2*Ek/m1) = sqrt(2*24/2.15) = 4.7249 m/s I don't quite understand what I may be doing wrong, some insight would be very much appreciated. Thanks in advance.