When fired from a gun, a bullet weighing 0.09 kg flew out at a speed of 800 m / s. On the flight of the bullet, 30%

When fired from a gun, a bullet weighing 0.09 kg flew out at a speed of 800 m / s. On the flight of the bullet, 30% of the energy received from the burnt gunpowder went. What was the mass of the burnt gunpowder?

Given: m1 (bullet mass) = 0.09 kg; V (bullet velocity when fired) = 800 m / s; η (the percentage of energy from the combustion of the powder, converted into the kinetic energy of the bullet) = 30% (0.3).

Constants: qp (specific heat of combustion of gunpowder) = 3.8 * 10 ^ 6 J / kg.

We express the mass of burnt powder from the formula: η = A / Q = ΔEk / Q = 0.5 * m1 * V ^ 2 / (qp * m ^ 2), whence m2 = 0.5 * m1 * V ^ 2 / (η * qp).

Calculation: m2 = 0.5 * 0.09 * 800 ^ 2 / (0.3 * 3.8 * 10 ^ 6) = 0.0253 kg (25.3 g).

Answer: The mass of the burnt powder was 25.3 g.