A lead bullet pierces the wall. Bullet speed before impact 350 m / s, after impact 200 m / s. The temperature of the bullet before impact is 300C. Find how much of the bullet’s mass has melted. The melting point of lead is 3270C, the specific heat is 130 J / kgK, and the specific heat of fusion is 25 kJ / kg.
V0 = 350 m / s.
V = 200 m / s.
t1 = 30 ° C.
t2 = 327 ° C.
C = 130 J / kg * ° C.
q = 25 * 103 J / kg.
mр / m -?
When a bullet breaks through a wall, part of its kinetic energy is converted into heat energy. The change in the kinetic energy of the bullet ΔEk goes to heating and melting the bullet Q.
ΔEk = Q.
Q = Q1 + Q2, where Q1 is the thermal energy for heating the bullet to the melting temperature, Q2 is the thermal energy that goes into melting itself.
Q2 = Q – Q1 = ΔEk – Q1.
ΔEk = m * V0 ^ 2/2 – m * V ^ 2/2 = m * (V0 ^ 2 – V ^ 2) / 2.
Q1 = C * m * (t2 – t1).
Q2 = q * mr.
q * mр = m * (V0 ^ 2 – V ^ 2) / 2 – C * m * (t2 – t1).
mр / m = (V0 ^ 2 – V ^ 2) / 2 * q – C * (t2 – t1) / q.
mр / m = ((350 m / s) ^ 2 – (200 m / s) ^ 2) / 2 * 25 * 10 ^ 3 J / kg – 130 J / kg * ° C * (327 ° C – 30 ° C) / 25 * 10 ^ 3 J / kg = 0.1.
Answer: when breaking through the wall, 0.1 of the mass of the bullet will melt: mp / m = 0.1.
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