You fire two bullets through a chronograph. The chronograph gives you speeds of

Question

You fire two bullets through a chronograph. The chronograph gives you speeds of the bullets. You loaded the cartridges, so you know the mass of the bullets. One bullet is slow and heavy. The other bullet is fast and light. You calculate that the two bullets have the same momentum when exiting the muzzle of your gun.

Which bullet loses more energy to air friction? Which bullet would penetrate deeper into the target, and which bullet would transfer more energy to the target?

Explanation / Answer

let mass,velocity of heavy one be M,U and for light weight be m,v since momentums are equal MU=mu u/U=M/m---->1 loss in energy =conversion of kinetic energy to other forms of energy K.E1=1/2*M*U^2 [for heavy one] K.E2=1/2*m*u^2 k.e1/k.e2=MU^2/mu^2 =(M/m)(U^2/u^2) =(M/m)(m/M)^2 =m/M hence kinetic energy inversely proportional to their masses.so more loss occur in light weight body than in heavy one. since penetrating force is same,deceleration produced in both same.hence the body with more speed penetrates more. hence light mass penetrate more than heavy one. since energy loss in light mass is more.the energy it transfer will be more

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