Math Problem

Sami

Recoil isn't calculated to the shooter but to the weapon. Do they give you the length of the barrel? You are not calculating work either, just force (F) so m*a should be enough based on the info given.

Serendipity

They don't give the length of the barrel.

All that's given in the problem is what I quoted in the original post.

I've been trying desperately to figure this out since it is due in 2 days and will be graded.

petrym

The average barrel length is what, 30-40 cm? After the bullet travels that far the gas is vented and doesn't matter anymore.

Serendipity

Well, the problem does not talk about barrel length so I don't think it is part of the calculations.

I'm starting to think this is straightforward - but I'm still unsure as to how to do the problem.

SCompRacer

I-SIG wrote: »

Actually the effects of recoil are cumulative.

I agree.

Serendipity

So does that mean the recoil force adds up to = 8 times the force of the first shot?

Deadof_knight

you have to figure out part the problem to get the last part, a given round has a known fps "feet per second value" and that said the weight of the bullet comes into play for the force applied to find out the distance traveled.

SCompRacer

I don't know the answer to your question, but recall from some full auto training that Newton’s Third Law may apply. The basic rule was shoot in shorter bursts to maintain accuracy to reduce muzzle rise. But as it has been mentioned, weapon design affects the ability to control it. All I remember from school daze is to not look too far past what was presented in the question. What I remember about actually shooting a full 30 round clip from an M-16 in a standing position is you had to continually lean into it to keep on target.

sophie

as i have only had general science i am not a lot of help as to this but somthing that might help: Ek=1/2 mv^2, that is kenetic energy(J) = 1/2 mass(Kg) times volicety(m/s) times volicety(m/s)
1J=1N*1M but i dont think distance helps much because in the calculations that is didtance strate up and not sidewase, as far as i know you can calculate with that unless you it is a straight line then you use the calculations for the simple machine inclined plane, wish i could help more but i cant do this with out more information, the acceleration would make this a quick calculation but without it i am stuck.

PolkThug

appadv wrote: »

I understand that F = m*a and that F = d(mv)/dt, but I'm unsure as to how to find the distance that the bullets traveled in the work equation. Since W = F*d and F = m*a, then Work should equal W = m*a*d.

Well why didn't you just say so in the first place? The answer is STFU MF.

Tex

This problem falls under the Impulse-Momentum Theorem. Average force = mv/t. The mass is 8*.00745kg. The velocity is actually the change in momentum which the initial velocity is 0 so the change is 293m/s. The time is how long it takes to fire the 8 rounds which is about .48 seconds. This will give you an average force of 36.38N (Newtons). The number of shots is not relevant. You can figure it with 1000 rds with t=60s and get the same answer. This means the equation could be simplified to f = mvr. I am not an expert but am pretty sure this is correct. Good luck!

Sami

0.00745 x 293 / (8*60/1000) N = 4.55N



Edit: Looks like Tex beat me to it and remembered to include the number of bullets, 8. 8*4.55 = 36.4

Serendipity

PolkThug wrote: »

Well why didn't you just say so in the first place? The answer is STFU MF.

Well, I didn't know how to find the distance, and Tex just figured out the problem.

Thanks Tex!

Serendipity

I'd like to thank you all for helping me solve this problem - I really appreciate it.

I don't know what kind of grade I would get if you guys didn't help me figure out the calculations, but anyways, I hope I get an A on the problem.

Again, thanks!

mrbigbluelight

Well, you're welcome, but .... I can't take ALL the credit.


....or can I ?

jdhdiggs

Thanks tex, I forgot about the change in momentum can substitute the Newtonian acceleration equations-Well done!.

(I burned all my physics and calc books when I left school and had forgot about that)

Recoil guys: He's talking about the recoil the weapon feels or the transfer of energy to the bullet. If the weapon is moving backwords/up and down, the bullet would lose speed as well since that is NOT included in the question, it should be assumed away. Remember that in physics and math, a horse is a cylinder and not a mammel with 4 legs.

Sami

jdhdiggs wrote: »

Thanks tex, I forgot about the change in momentum can substitute the Newtonian acceleration equations-Well done!.

I thought it's still the same equation m * dv/dt? Change in time, dt, is the rate of the fire.

mass = 0.00745 kg
dv = (293 - 0) m/s
dt = 60/1000 s = 0.06 s

The number of bullets cancel each other out in the equation so it's not relevant.

0.00745 kg * 293 m/s / 0.06 s = 36.38 kgm/s^2 = 36.4 N

audiobliss

What calculus is this? Calc 2?

Very interesting question...don't think I could have figured it out with a lot of input, either. Hope you get a good grade on it!

bikezappa

Just saw this.

F=ma or the recoill force of the bullet = the mass of bullet times it's acceleration.

Bullet starts with V1=0 as it leaves the barrel V2=293m/s

Time for bullet to travel (accelerate) is 60seconds/1000bullets

a=dv/dt or (V1-V2)/time for bullet in barrel

F=(7.45g)a

plug and chug

Did that help?

Serendipity

audiobliss wrote: »

What calculus is this? Calc 2?

Very interesting question...don't think I could have figured it out with a lot of input, either. Hope you get a good grade on it!

Its differential calculus with physical applications. Part of my electrical engineering program.

Don't know what it is called, Calc 2 maybe?

audiobliss

appadv wrote: »

Its differential calculus with physical applications. Part of my electrical engineering program.

Don't know what it is called, Calc 2 maybe?

Sounds interesting enough, for sure. I'm not sure how the different Calc courses are broken up at different schools, but according to my experience Calc 1 is differentiation, Calc 2 is integration, and Calc 3 is three-dimensional applications of 1 & 2.

I haven't gotten into any physics yet, though. At least no more than the small amount of physics necessary to do some of the problems in math.

Sami

Yes, it's more of a physics problem than math. Wait until you get to the part where you need to calculate all the applicable forces...

I'm still having nightmares of my 'Solid mechanics' classes. Ever tried to calculate forces applied to a bridge? LOL

Serendipity

Well, I did differentiation and integration in HS, so maybe Calc 3? Again, the courses are not numerical at all schools...

audiobliss, are you the same audiobliss from the Definitive Technology forum?

jdhdiggs

Sami wrote: »

Yes, it's more of a physics problem than math. Wait until you get to the part where you need to calculate all the applicable forces...

I'm still having nightmares of my 'Solid mechanics' classes. Ever tried to calculate forces applied to a bridge? LOL

Pffft, statics was a freakin snap, I'd due trusses and structural work all day long as long as I could stay out of AC circuits and dynamic physics.

Sami

jdhdiggs wrote: »

Pffft, statics was a freakin snap, I'd due trusses and structural work all day long as long as I could stay out of AC circuits and dynamic physics.

Different strokes for different folks.

I'm a software engineer now and my main goal is to stay away from DSP's (I work with RX's and TX's all day). They say it's not that bad but one look at those algorithms is enough to scare me away...

Serendipity

Yeah, I know the AC circuits and dynamic physics stuff can be pretty hard.

I've still got 9 years of school left though.

audiobliss

appadv wrote: »

Well, I did differentiation and integration in HS, so maybe Calc 3? Again, the courses are not numerical at all schools...

audiobliss, are you the same audiobliss from the Definitive Technology forum?

Nope, never been on that forum. I also did Calc 1 and Calc 2 in HS.

appadv wrote: »

I've still got 9 years of school left though...right now I am a bit younger than Sid (Vr3MxStyler2k3)

What?! So, wait a minute...how old are you? Where are you schooling? Are you some kind of genius?! :eek:

Serendipity

Interesting... there was an audiobliss on the Def Tech forum some 2-3 years ago. I think he was also from NC.

I don't want to give away my age or location.

Sami

audiobliss wrote: »

What?! So, wait a minute...how old are you? Where are you schooling? Are you some kind of genius?! :eek:

I think we started with those kinds of test questions around 15-16y of age (I went to school in Europe). The way it is worded can be confusing and you might think of it as a more complex problem. I think that's part of the idea too.

Serendipity

I agree the question was confusing and made it seem like a more complex problem.