A bullet of mass 120 grams is fired into a target with a velocity of 400 m/s. The mass of the target is 10kg and it is free to move Find the loss of kinetic energy?
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Momentum is conserved. Initial momentum p is:
p=mv0=(0.12)(400)=48 kg m/s
Final momentum is the same, therefore:
p=(M+m)vf=48
Therefore final velocity vf is:
vf=4810+0.12=4.74308 m/s
Initial kinetic energy Ek0 is:
Ek0=12mv20=(0.5)(0.12)(4002)=9600 joules
Final kinetic energy Ekf is:
Ekf=12(M+m)v2f=(0.5)(10.12)(4.743082)=113.83 joules
Therefore the loss in kinetic energy ΔEk is:
ΔEk=Ek0−Ekf=9600−113.83
= 9486.17 joules
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