A lead bullet flying at a speed of 200 m / s hits an obstacle and gets stuck in it. By how many degrees did the bullet

A lead bullet flying at a speed of 200 m / s hits an obstacle and gets stuck in it. By how many degrees did the bullet temperature rise if 78% of the kinetic energy passed into its internal energy?

Bullet kinetic energy:

E = M V ^ 2/2,

where M is the mass of the bullet; V is the bullet velocity; V = 200 m / s.

The increase in the internal energy of the bullet is equal to: ΔU = 0.78 E = 0.39 M V ^ 2.

On the other hand: ΔU = c М ΔТ,

where c is the specific heat capacity of lead, c = 130 J / (kg × oC); ΔТ – bullet temperature rise, оС.

Thus, 0.39 M V ^ 2 = c M ΔT, whence the temperature rise:

ΔТ = 0.39 V ^ 2 / c = 0.39 × 200 ^ 2/130 = 120 oC.

Answer: ΔТ = 120 oC.