Question

A machine gun fires 360 bullets per min and each bullet travels with a velocity of 60m/s of the mass of each bullet is 5gm find the power of the machine gun?

Answer 1

Answer: Given,

Number of bullets, n=360nos.

Mass of bullet, m

Power, =5400watt

Kinetic energy of 360 bullets, K.E=n×  

2

1

​  

mv  

2

=360×  

2

1

​  

×m×600  

2

=648×10  

5

mJ

Power=  

time

kineticenergy

​  

 

5400=  

60

648×10  

5

m

​  

 

m=5×10  

−3

kg=5gram

Hence, weight of each bullet is 5gram

Answer 2

Answer:

A machine gun fires 360 bullets per min and each bullet travels with a velocity of 60m/s of the mass of each bullet is 5gm. The power of the machine gun will be $54 \ Watt$.

Explanation:

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

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

From the question,

$m = 5 g = 5\times 10^{-3} kg$

$v= 60\ m/s$

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

   $=\frac{360}{ 60\ s} = 6\ bullets\ per\ s$

Substitute the above values into equation(2)

Equation (2) becomes,

$P= 6 \times \frac{1}{2}\times 5\times10^{-3} \times 60^{2}$

   $= 54\ Watt$

The power of the gun $= 54\ Watt$