A 6.0-kg object, initially at rest in free space, \"explodes\"into three fragmen

Question

A 6.0-kg object, initially at rest in free space, "explodes"into three fragments of equal mass. Two of these fragments areobserved to be moving with equal speeds of 20 m/s with an angle of60 degrees between their direction of motion. How much kineticenergy is released during this explosion. Can someone please help? I do understand there is conservation of momentum, becauseForce (external ) is equal to 0. But , I don't know where to go from there. Thanks! A 6.0-kg object, initially at rest in free space, "explodes"into three fragments of equal mass. Two of these fragments areobserved to be moving with equal speeds of 20 m/s with an angle of60 degrees between their direction of motion. How much kineticenergy is released during this explosion. Can someone please help? I do understand there is conservation of momentum, becauseForce (external ) is equal to 0. But , I don't know where to go from there. Thanks!

Explanation / Answer

we can break this down into a conservation of momentum problem,each mass is 2.0 kg and their directions of travel. picture theirtrajectories making the shape of a peace symbol with the pointwhere they all meet being their point of origin. the x component ofthe bottom two cancel out so we know that the final mass will movestraight up from the origin (i.e. it will have no x-component ofvelocity). the two bottom masses will have a momentum equal to2.0kg * 20 m/s = 40 kgm/s and a y-component of momentum equal to40kgm/s sin(30) = 35kgm/s and because there are two of themtraveling in the negative y-direction with the same momentum we candouble this value and call it to total y-momentum because of thesetwo masses, so the top mass will have an equal momentum to satisfythe conservation of momentum law. so 2.0 kg (v) = 70 kgm/s v = 35 m/s now we add the kinetic energies 1/2 m v2 for each massgives us m1=400 J m2=400 J m3(top mass) = 1225 J energy = 2025j

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