Question

a machine gun fires 240 bullets per minute with a velocity 500m/s.If the mass of each bullet is 500grams, the power of the gun is​

Answer 1

Answer:

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Answer 2

Answer:

A machine gun fires 240 bullets per minute with a velocity of 500m/s. If the mass of each bullet is 500grams, the power of the gun is​ $250\ KW$

Explanation:

The power of the gun is the rate of work done or the amount of energy converted per unit time.

It can be expressed as,

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 written as,

$K.E = \frac{1}{2} m v^{2}$  

where m - The mass of the bullet  and

           v - velocity

Let n be the number of bullets,

then power becomes,

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

That is,

$P= \frac{n}{t} \times \frac{1}{2} m v^{2}$    ...(3)

From the question,

$m = 500\ g = 0.5\ kg$

$v= 500\ m/s$

$\frac{n}{t} = \frac{240\ bullets}{minute}$

   $=\frac{ 240}{60\ s} = 4\ bullets\ per\ second$

Substitute the above values into equation(3)

We get,

$P= 4\times \frac{1}{2} \times0.5\times 500^{2}$

    $= 250000\ Watt = 250\ KW$

        

• The power $250\ KW$