Calculating Average Recoil Force for Machine Gun Firing 50g Bullets

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Homework Help Overview

The discussion revolves around calculating the average recoil force experienced by a machine gun firing 50-gram bullets at a rate of 4 bullets per second, with each bullet leaving the gun at a speed of 1000 m/s. Participants are exploring the relationship between impulse, momentum, and force in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between impulse and force, questioning how to apply Newton's laws and the definitions of momentum and average force. There are attempts to clarify the correct equations and units needed for the calculations.

Discussion Status

Some participants have provided guidance on the correct application of formulas and units, while others are still grappling with the calculations and assumptions. There is an ongoing exploration of different interpretations of the problem setup and the equations involved.

Contextual Notes

Participants are navigating potential confusion regarding unit conversions and the time frame for the calculations, as well as the implications of using multiple bullets versus a single bullet in their reasoning.

gcombina
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A machine gun fires 50-g bullets at the rate of 4 bullets per second. The bullets leave the gun at a speed of 1000 m/s. What is the average recoil force experienced by the machine gun?

My attempt:
(1) J = FT
F= J/T

so what else should I do?
 
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Well average velocity is total distance divided by total time ... what would average force be?
(Hint: Newtons laws ... how is force related to change in momentum?)
 
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F= J/T= mv/T

Thanks!
 
Well done.
Just checking:- if you traveled in 10s bursts of 10m/s which occur 90s apart - what's the average speed?
The problem you have is actually slightly easier than that.
 
Hello, so I get 200000 g m/s,

what am I doing wrong?
 
Please show your working.
 
J = ft
= (mv) t
= (200g * 1000 m/s) (1s)
= 200 000 gm

* its asking me for the recoil which means the impulse right?
and that is J = ft and what is force? f = mv right? so final formula is J = (mv) (t)
* mass is 200g because of the 4 bullets and velocity is 1000m/s

so I don't know why is wrong, can't see it
 
gcombina said:
J = ft
= (mv) t
Check that equation (J=mvt) by dimemsional analysis.

If "f" is the force in that equation, then you just wrote "force=momentum" ... which is incorrect.
If J is specific impulse, then ##J=\Delta p##

* its asking me for the recoil which means the impulse right?
No - it specifically asks for the average force of the recoil. $$\bar F = \frac{\Delta p}{\Delta t}$$

and that is J = ft and what is force? f = mv right?
No, ##F=ma##.

* mass is 200g because of the 4 bullets and velocity is 1000m/s
Or just use one bullet averaged over 0.25s ... whatever, should get the same number.
But use the right equation, you'll get the right units.
 
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ok

ok I did

F = Δp / Δt

but still I am getting the same bad answer

F = (200 gr/s) (1000 m/s) / (1s)

what is wrong with my equation?
 
  • #10
where did 1 second come from? I did't see that anywhere in the problem.
 
  • #11
gcombina said:
ok I did

F = Δp / Δt

but still I am getting the same bad answer

F = (200 gr/s) (1000 m/s) / (1s)

what is wrong with my equation?

Besides the fact that you're mysteriously dividing by (1s), there seems to be nothing wrong with it.
 
  • #12
cause my equation is F = mv/t

so the time is 1 second (all bullets fired in one second), what else should I put then? any ideas?
 
  • #13
F = (200 gr/s) (1000 m/s) / (1s)
Are you not expected to give Force in SI units?
How do you know you got he wrong answer?
 
  • #14
@Simon, ok i needed to convert 200 gr into kg which is .20 kg and I got 200 N.
Thanks!
 

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