Calculate Bullets Per Minute for Machine Gun and Man

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In summary: CIn summary, the first part of the conversation involved calculating the speed of a block after 15 bullets are fired at it by a machine gun. The second part involved determining the maximum number of bullets a man can fire per minute while exerting an average force of 180 N against the gun. The equation used for this calculation was F*t=m*v, and the result was 176 bullets per minute. However, this may cause the force on the shooter to exceed 180N.
  • #1
blue5t1053
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This was a two part question, the first part I was able to calculate.

Question Part 1:
A machine gun fires a stream of bullets into a block that is free to move on a horizontal frictionless tabletop. Each bullet has mass 66 grams; their speed is 930 m/sec, and the block a mass of 7.36 kg. After 15 bullets, the speed of the block is?

Calculation Part 1:
[tex]\frac{(0.066 kg * 15 bullets)}{(0.066 kg * 15 bullets) + 7.36 kg}=110.263 m/sec[/tex]

Question Part 2:
If a man in the previous statement can exert an average force of 180 N against the gun, determine the maximum number of bullets he can fire per minute.

Attempt to Calculate:
I am unsure of how I would go about this. I attempted to think of it as a reverse of the previous question, but what didn't work out was getting bullets per minute without figuring out a basic equation then using sample bullets/minute numbers to see where the breaking point of 0 m/sec is. Also, I kept in mind the need to change the velocity of m/sec to m/min if needed.

The equation I attempted to use was:
[tex]V_{gun+man}=\frac{m_{bullet}*numberofbullets}{(m_{bullet}*numberofbullets)+M_{man}}v_{bullet}[/tex]

Any help with where to start?
 
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  • #2
it is basically just a simple problem of conservation of momentum.
 
  • #3
You have the "force equation": F*t=m*v
the total momentum during a minute is m*v*k, where k is the number of bullets per minute.
 
  • #4
Kurret said:
You have the "force equation": F*t=m*v
the total momentum during a minute is m*v*k, where k is the number of bullets per minute.


So I get...

[tex]F \times t=m \times v[/tex]

[tex]F \times t=m \times v \times k[/tex]

[tex]\frac{F \times t}{m \times v}=k; k=bullets/min[/tex]

[tex]\frac{180 N \times 60 sec}{0.066 kg \times 930 m/sec}=175.953 bullets/sec[/tex]


Thank you both.
 
  • #5
blue5t1053 said:
So I get...

[tex]F \times t=m \times v[/tex]

[tex]F \times t=m \times v \times k[/tex]

[tex]\frac{F \times t}{m \times v}=k; k=bullets/min[/tex]

[tex]\frac{180 N \times 60 sec}{0.066 kg \times 930 m/sec}=175.953 bullets/sec[/tex]Thank you both.

.953?
Never knew Bullets went to the target in fractions.!
 
  • #6
ever heard of splinters/shotguns/shells
 
  • #7
Part 1 is correct, although your expression is not correct. You need the muzzle velocity in there:

[tex]m_{bullet}v_{muzzle} N_{bullets} = \Delta P = (M_{block} + m_{bullet}N_{bullets}) v_{block/bullets}[/tex]

The analysis for Part 2 is not clear.Since the force applied by the gun to the shooter is the time rate of change of momentum of the gun/bullet system F = dp/dt:

[tex]F = \frac{dm}{dt}v_{muzzle}[/tex]

[tex]\frac{dm}{dt} = F/v = 180/930 = .194 \text{kg/sec}[/tex]

Therefore, the number of bullets per second is .194/.066 = 2.94 or 176 bullets/minute, but this is only if you want to provide an average force of 180 N. The actual peak force that must be applied will be greater than this, so actually firing this number of bullets will cause the force on the shooter to exceed 180N.

AM
 
Last edited:

1. How do you calculate the bullets per minute for a machine gun?

To calculate the bullets per minute for a machine gun, you need to know the rate of fire for the gun, which is usually measured in rounds per minute (RPM). This information can usually be found in the gun's manual or on the manufacturer's website. Once you have the RPM, simply divide it by 60 to get the bullets per minute.

2. What factors can affect the bullets per minute for a machine gun?

The main factors that can affect the bullets per minute for a machine gun are the rate of fire, the type and size of the ammunition being used, and the condition of the gun. Additionally, external factors such as temperature, humidity, and altitude can also have an impact on the gun's performance.

3. How does the size and type of ammunition affect the bullets per minute for a machine gun?

The size and type of ammunition being used can greatly impact the bullets per minute for a machine gun. Generally, larger and heavier bullets will decrease the RPM, as they require more force to be fired and may take longer to reload. On the other hand, smaller and lighter bullets may increase the RPM, as they require less force and may be easier and faster to reload.

4. Can a person fire a machine gun at the same rate as a machine?

No, a person cannot fire a machine gun at the same rate as a machine. Machine guns are designed to fire at a high rate of fire for extended periods of time, while a person's physical abilities and stamina will limit their ability to sustain a high rate of fire. Additionally, machine guns are often mounted on tripods or other stable platforms, while a person firing a gun will have to account for recoil and movement, which can also affect the rate of fire.

5. How does the rate of fire for a machine gun compare to that of a man?

The rate of fire for a machine gun is significantly higher than that of a man. A typical machine gun can fire between 600-1000 rounds per minute, while a person can generally fire between 60-120 rounds per minute. This is due to the mechanical advantage and efficiency of a machine gun compared to a person's physical abilities.

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