A machine gun fires 360 bullets per minute and each bullet travels with a velocity of 600 m s⁻¹. If the mass of each bullet is 5 gm, find the power of the machine gun?
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mass of each bullet , m = 5g = 0.005Kg
number of bullets are fired by machine gun = 360 /min = 360/60sec = 6/sec
so, bullets are fired in t sec, n = 6t
now, mass of all bullets, M = nm = 0.005 × 6t = 0.03t kg
kinetic energy of all bullets = 1/2Mv²
= 1/2 × 0.03t × (600)²
= 1/2 × 0.03t × 360000
= 1800 × 3t
= 5400t joule
now, power = energy/time taken
= 5400t/t = 5400W or 5.4kW
hence, power of the machine gun = 5.4kW
number of bullets are fired by machine gun = 360 /min = 360/60sec = 6/sec
so, bullets are fired in t sec, n = 6t
now, mass of all bullets, M = nm = 0.005 × 6t = 0.03t kg
kinetic energy of all bullets = 1/2Mv²
= 1/2 × 0.03t × (600)²
= 1/2 × 0.03t × 360000
= 1800 × 3t
= 5400t joule
now, power = energy/time taken
= 5400t/t = 5400W or 5.4kW
hence, power of the machine gun = 5.4kW
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