Question

A machine gun fires 360 bullets per minute and each bullet travels with a velocity of ${600m}^{s-1}$ . If the mass of each bullet is 5 gm , find the power of the machine gun.​

Answer 1

No. of bullets (n) = 360

velocity (v) = 600 m/s

mass of of the bullet (m) = 5 gr = 5 × ${10}^{-3}$ kg

time (t) = 1 m = 60 s

from the definition of power

• P = $\frac{W}{t}$

Here, kinetic energy stored as a work done

:. P = $\frac{K.E}{t}$ = $\frac{½mv² × n}{60}$

• $\frac{½*5*10-³*(600)²*360}{60}$

• $\frac{½*5*10-³*600*600*360}{60}$

• $\frac{½*5*36*10⁴*10-³*36*10¹}{60}$

• $\frac{5*18*36*10²}{60}$

• 18 × 3 × 10²
• 54 × 10²
• 5400

• $\frac{5400}{1000}$

• $\frac{ 54 }{ 10 }$

P = 5.4 kw