Question

A machine gun fires 360 bullets per minute and each bullet travels with a velocity of 600 ms-1. If the mass of each bullet is 5gm, find the power of the machine gun? ​

Answer 1

Answer:

Power of the machine gun is 5400w

Here n = 360 ,

't = 60 sec,

V = 600 ms−1

m =5g =5×10 −3 kg Power,

p=K.E of n bulletst =1/2mnV^2 t

 

=12×5×10−3×360×600×60060

∴

P=5400,

W=5.4KW

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Answer 2

Answer:

A machine gun fires 360 bullets per minute and each bullet travels with a velocity of 600 ms-1. If the mass of each bullet is 5gm. The power of the machine gun will be  $5400\ Watt$

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 given by,

$K.E = \frac{1}{2} m v^{2}$  

where m -  the mass of the bullet  

           v - velocity

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)

where n is the number of bullets.

In the question, it is given that,

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

$v= 600m/s$

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

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

Substitute the above values into equation(2)

Equation (2) becomes,

$P= 6 \times \frac{1}{2}\times 5\times10^{-3} \times 600^{2}$

   $= 5400\ Watt$

The power of the gun $= 5400\ Watt$