Calculating Average Recoil Force for Machine Gun Firing 50g Bullets

[gcombina]

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?

 

[Simon Bridge]

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?)

 

[gcombina]

F= J/T= mv/T

Thanks!

 

[Simon Bridge]

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.

 

[gcombina]

Hello, so I get 200000 g m/s,

what am I doing wrong?

 

[Simon Bridge]

Please show your working.

 

[gcombina]

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

 

[Simon Bridge]

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.

 

[gcombina]

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?

 

[dauto]

where did 1 second come from? I did't see that anywhere in the problem.

 

[dauto]

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.

 

[gcombina]

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?

 

[Simon Bridge]

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?

 

[gcombina]

@Simon, ok i needed to convert 200 gr into kg which is .20 kg and I got 200 N.
Thanks!