Muzzle velocity of a pistol

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In summary: I understand now what you did here. 5.314/0.00648 = 820.06, so I guess you just forgot to include the '06'?2. I'm still not sure why this is wrong, but I don't know what else to try, I don't know what the other equation is, if you could give me it, I'll try it.Thank you1) Yes, I forgot the 0.06 in the end. That's not significant.2) The bullet was embedded. That means that after the collision, the bullet and the block of wood moved together. If v is the
  • #1
lando45
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In an arrangement for measuring the muzzle velocity of a rifle or pistol, the bullet is fired up at a wooden mass, into which it embeds. The wood is blasted straight up into the air to a measured height h. Assuming negligible losses to friction, write an expression for the velocity in terms of the known masses and height. Use mb for the mass of the bullet, mw for the mass of the wood, h for height and g for gravity.

I got this question set in my college course, and we haven't even begun to cover momentum etc. yet, so I don't really have any ideas of how to go about answering this...any help please? Thanks a lot.
 
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  • #2
i would have thought that was an energy conservation question,
think KE and PE
 
  • #3
So m x g x h? And/or 1/2mvsquared?
 
  • #4
Ah ok I cracked it, I got the formula:

sqrt(2gh)+(mw*sqrt(2gh))/(mb)

which appears to be correct. However, part b) of the question is this:

If a 100 grain (6.48 g) 25-06 Remington rifle bullet is fired into a 4.72 kg block that then rises 4.4 cm into the air, what was the muzzle velocity of that bullet?

I tried feeding all the values into the above formula:

g = 9.81
h = 0.044
mw = 4.72
mb = 0.00648

And I got a velocity answer of 820m/s which my teacher tells me is wrong...anyone know what I'm doing wrong? Thanks
 
  • #5
Please, does anyonw know why 820m/s is wrong? This is my working:

sqrt(2gh)+(mw*sqrt(2gh))/(mb)

sqrt(2 x 9.81 x 0.044) + (4.72 x sqrt[2 x 9.81 x 0.044])
-----------------------------------------------------
0.00648

0.929 + 4.285
--------------
0.00648

5.314
------
0.00648

= 820 m/s

But this answer isn't right! How is it not right?! Am I using all the correct units? Thanks
 
  • #6
im not sure where u got that formula

but the formula i get is 0.5mv^2(of bullet) + 0.5mv^2(of wood) = mgh(of bullet) + mgh(of wood)

the kenetic energy of the wood initially is zero so u can simplify equation to..

0.5mv^2(of bullet) = mgh(of bullet) + mgh(of wood)
further simplify to..
0.5mv^2 = (Mb + Mw)gh

and you have to remember that if the bullet is embeded in the wood then for mgh you must use mass of both bullet and wood.

can u explain how you got your equation?
 
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  • #7
0.5mv^2 = (Mb + Mw)gh

So 0.5mv^2 = 2.04

What does the '^' represent in your equation?
 
  • #8
alias25 said:
i would have thought that was an energy conservation question,
think KE and PE
Energy cannot be assumed to be conserved in collisions (unless otherwise stated, as in elastic). Therefore the problem is not purely about KE and PE.

To the original poster: Have you ever used the conservation of momentum principle?
 
  • #9
I got my equation with some help from my teacher, although I didn't fully understand his explanation of why...but he said that was defintely the correct forumla, which doesn't explain why I'm getting the wrong answer. Maybe your formula will help...
 
  • #10
'^' represents 'to the power of..'
wel if ur teacher says it's definatly the correct equation, who am i to argue, I am only a 6th form student.
conservation of momentum would work actually i think mu+mu = mv+mv
hang on you would need finial velocity would that be '0'? that complicates things
b right back
 
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  • #11
Päällikkö said:
Energy cannot be assumed to be conserved in collisions (unless otherwise stated, as in elastic). Therefore the problem is not purely about KE and PE.

To the original poster: Have you ever used the conservation of momentum principle?

Yes, is that what I should be using for this?
 
  • #12
alias25 said:
'^' represents 'to the power of..'
wel if ur teacher says it's definatly the correct equation, who am i to argue, I am only a 6th form student.
conservation of momentum would work actually i think mu+mu = mv+mv
hang on you would need finial velocity would that be '0'? that complicates things

By using your original formula I got an answer of 25, which I'm fairly sure is wrong, and as I only have 1 submission left, I don't want to use it unless I'm absolutely sure! The Conservation of momentum sounds good, but isn't it mu1 + mu2 = vu1 + vu2? Because surely mu + mu = vu + vu is equal ro mu = vu which means m = v?
 
  • #13
lando45 said:
By using your original formula I got an answer of 25, which I'm fairly sure is wrong, and as I only have 1 submission left, I don't want to use it unless I'm absolutely sure!
That's what I get using the conservation of energy principle, which in this case ought to be wrong.

The Conservation of momentum sounds good, but isn't it mu1 + mu2 = vu1 + vu2? Because surely mu + mu = vu + vu is equal ro mu = vu which means m = v?
No.
I've got no idea what the v's and u's are in your equation (normally used for velocities in conservation of momentum). Momentum: [itex]\vec{p}= m \vec{v}[/itex]
 
  • #14
Ah I'm even more confused than ever now, so which formula should I be using to solve this question?:

If a 100 grain (6.48 g) 25-06 Remington rifle bullet is fired into a 4.72 kg block that then rises 4.4 cm into the air, what was the muzzle velocity of that bullet?

Thanks
 
  • #15
lando45 said:
Ah I'm even more confused than ever now, so which formula should I be using to solve this question?:
If a 100 grain (6.48 g) 25-06 Remington rifle bullet is fired into a 4.72 kg block that then rises 4.4 cm into the air, what was the muzzle velocity of that bullet?
Thanks

Normally, you are supposed to use conservation of momentum (and after collision, conservation of energy). See the case "totally inelastic collision" (refer to your physics book or google). Energy is lost during collisions of that type.

I'm confused too: Your teacher has helped you with what seems to be an equation of conservation of energy. This is not the way to approach a collision problem, but then again, if you've not been teached the conservation of momentum, how could you use it?
 
  • #16
from the formula you given ...

( sqroot(2gh) + Mw(sqroot(2gh) )/Mb = v

i rearrage..

vMb = sqroot (2gh) + Mw(sqroot(2gh)) ...to..

vMb = (sqroot(2gh)) *( 1 + Mw)

we know from simplifiying mgh = 0.5mv^2 that v = sqroot(2gh)
so..

vMb = V ( 1 + Mw)

vMb = V + vMw
and that is as much as i can get close to conservation of momentum

and i think its wrong too. i don't know it might help u figure something out
 

1. What is muzzle velocity?

Muzzle velocity is the speed at which a bullet exits the barrel of a pistol or any other firearm. It is typically measured in feet per second (fps) or meters per second (m/s).

2. How is muzzle velocity measured?

Muzzle velocity is measured using a chronograph, which is a device that uses sensors to record the speed of a bullet as it passes through.

3. What factors affect muzzle velocity?

The muzzle velocity of a pistol is affected by several factors, including the type of ammunition used, the length and condition of the barrel, and the amount of gunpowder in the cartridge.

4. Is a higher muzzle velocity always better?

Not necessarily. While a higher muzzle velocity can result in a longer range and more impact force, it also means more recoil and potentially less accuracy. The optimal muzzle velocity depends on the intended use of the pistol.

5. Can the muzzle velocity of a pistol be increased?

Yes, the muzzle velocity of a pistol can be increased by using higher quality ammunition, optimizing the barrel length and condition, and adjusting the amount and type of gunpowder used in the cartridge. However, it is important to note that altering the firearm's original specifications can have safety and legal implications.

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