A bullet of mass m moving with velocity u
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a bullet of mass m moving with a velocity u strike a block of mass M at rest and gets embedded in the block .the loss of kinetic energy in the impact is.
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m = mass of bullet
u = initial velocity of bullet before the collision
M = mass of block
V = final velocity of bullet-block combination after collision
Using conservation of momentum
m u = (m + M) V
V = m u/(m + M) eq-1
KE₁ = initial kinetic energy = (0.5) m u²
KE₂ = final kinetic energy = (0.5) (m + M) V²
Loss of kinetic energy is given as
ΔKE = KE₁ - KE₂
ΔKE = (0.5) m u²- (0.5) (m + M) V²
using eq-1
ΔKE = (0.5) m u²- (0.5) (m + M) (m u/(m + M) )²
ΔKE = (0.5) m u²- (0.5) m² u²/ (m + M)
ΔKE = ((0.5) m² u² + (0.5) m M u²- (0.5) m² u²)/(m + M)
ΔKE = (0.5) m M u²/(m + M)
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