Is it possible for a lead bullet to completely melt when fired by a rifle at a f

Question

Is it possible for a lead bullet to completely melt when fired by a rifle at a fixed target? Assume that the bullet is initially at a temperature of 25o C, all the initial kinetic energy of the bullet is converted to heat when it strikes the target and that no heat flows from the bullet to its surroundings. The specific heat capacity of lead is 130 J K1 kg1, its heat of fusion is 24.5 × 103 J kg1 and its melting point is 327.3 oC. Calculate the minimum speed of the bullet so that the heat developed when it is brought to rest will be just sufficient to completely melt it. For comparison, typical rifles have muzzle speeds that exceed the speed of sound in air, which is 347 m/s at 25o C. Do you think it is possible for a lead rifle bullet to completely melt when hitting a target?

Explanation / Answer

Let mass of bullet be m

Total ebergy requied to melt = energy required to reach 327.3 C from 25 C + Heat of fusion

Etotal = mCdT + mH

Etotal = m*(327.3 - 25) *130 = 39299m + 24500*m = 63799m

By conservation of energy Etotal = initial knetic energy

63799m = 1/2mv2

v2 = 127598

v = 357.2 m/s

this is the minimum speed of bullet required to completely melt.

Since typical speed of bullet exceeds speed of sound which is 347 m/s and required speed is nearly same i.e. 357.2 m/s hence it is possible for a lead rifle bullet to completely melt when hitting a target.

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