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Question Video: Finding the Momentum Transferred per Second to Fired Bullets given the Mass of a Bullet and the Firing Rate Mathematics

A gun fires 97 bullets per minute. The mass of each bullet is 10 g, and the muzzle speed of the gun is 180 m/s, where the muzzle speed is the exit speed of the bullet from the barrel of the gun. Find the momentum transferred to the bullets per second.

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Video Transcript

A gun fires 97 bullets per minute. The mass of each bullet is 10 grams, and the muzzle speed of the gun is 180 meters per second, where the muzzle speed is the exit speed of the bullet from the barrel of the gun. Find the momentum transferred to the bullets per second.

We begin by recalling that the momentum 𝐻 is equal to the mass 𝑚 multiplied by the velocity 𝑣, where the standard units for mass are kilograms and the standard units for velocity are meters per second. The momentum 𝐻 is therefore measured in kilogram meters per second.

We are told in this question that the mass of the bullet is 10 grams and its velocity is 180 meters per second. We know that there are 1000 grams in a kilogram. Dividing 10 by 1000, we see that 10 grams is equal to 0.01 kilograms. We can now calculate the momentum of the bullet by multiplying 0.01 by 180. This is equal to 1.8 kilogram meters per second.

We might think that this is the final answer. However, there is one more piece of information that we have not considered. We are told that the gun fires 97 bullets per minute. There are 60 seconds in one minute. This means that if the gun fires 97 bullets per minute, it fires 97 over 60 bullets per second. So if each bullet has been given 1.8 kilogram meters per second of momentum and there are 97 over 60 or just over 1.6 of them leaving the gun per second, then the momentum transferred per second is 1.8 multiplied by 97 over 60. This is equal to 2.91 kilogram meters per second.

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