A machine gun fires 60 bullets per minute, with a velocity of 700 m/s .If each bullet has a mass of 50 g .Find the power developed by the gun​

 To calculate the power developed by the gun, you need to know that power is the work done per unit time. When the gun fires bullets, it does work on each bullet by imparting kinetic energy to them. The kinetic energy (KE) for each bullet can be calculated using the formula:

KE = (1/2) * m * v^2

where m is the mass of the bullet and v is the velocity of the bullet.

The power (P) can be found through the formula:

P = Work/Time

Since the work done on each bullet is equal to its kinetic energy, we can replace Work with the total kinetic energy imparted to all the bullets fired in one minute.

Let's calculate the power step by step:

Step 1: Calculate the kinetic energy for one bullet: - Mass of the bullet (m) = 50 g = 0.05 kg (since 1 kg = 1000 g) - Velocity of the bullet (v) = 700 m/s

KE per bullet = (1/2) * m * v^2 KE per bullet = (1/2) * 0.05 kg * (700 m/s)^2 KE per bullet = 0.025 kg * 490000 m^2/s^2 KE per bullet = 12250 J (Joules)

Step 2: Calculate the total kinetic energy for all bullets fired in one minute: - Bullets per minute = 60

Total KE = KE per bullet * Bullets per minute Total KE = 12250 J/bullet * 60 bullets Total KE = 735000 J

Step 3: Calculate the power: - Time (t) = 1 minute = 60 seconds

Power (P) = Total KE / t P = 735000 J / 60 s P = 12250 J/s P = 12250 W (Watts)

So, the power developed by the gun is 12250 W.