Question

a machine gun fires 360 bullets per minute each bullet moves with velocity of 600ms if the power of the gun is 5.4Kw the mass of each bullet is

Answer 1

Power of gun = no of bullets fired in 1 sec × kinetic energy of each bullet

5.4 ×1000 = 360/60 × 1/2 m (600)^2

m = 0.5 ×10^-3 kg

m = 0.5 g

Answer 2

Answer:

A machine gun fires 360 bullets per minute each bullet moves with velocity of 600ms if the power of the gun is 5.4Kw the mass of each bullet is $5\ g$.

Explanation:

Power of the gun can be simply defined as the rate of work done or the amount of energy converted per unit time.

Power (P)  $= \frac{Work\\ done\ (W)}{time\ (t)}$  ...(1)

Work done by the bullet will be equal to the change in kinetic energy which can be expressed as,

$K.E = \frac{1}{2} m v^{2}$  

where m - The mass of the bullet  

           v - velocity

Let n be the number of bullets,

then power becomes,

$\text { Power }=n \times \frac{\frac{1}{2} m v^{2}}{t}$

Or

$P= \frac{n}{t} \times \frac{1}{2} m v^{2}$    ...(2)

Rearranging,

$m = \frac{2P}{v^{2} } \times\frac{t}{n}$        ....(3)

From the question,

$v= 600\ m/s$

$\frac{t}{n} = \frac{minute}{360\ bullets}$

   $=\frac{ 60\ s}{360} = \frac{1s}{6\ }$

$P = 5.4KW =5.4\times 10^{3} \ Watt$

Substitute the above values into equation(3)

Equation (3) becomes,

$m = \frac{2\times 5.4\times 10^{3} }{600^{2} } \times\frac{1}{6}$

     $= 0.005 \ kg = 5\ g$

   

• The mass of the bullet $= 5\ g$