i'm usually pretty good at math, but i'm stumped

[unclejed613]

here's the problem: an 8lb object traveling at 1000ft/sec has what energy in ft-lb?

formula E=½*m*v²

my calculation yields 8(1000*1000)*0.5=4,000,000ft-lb

a co-worker's calculation converts to grains and divides by a "fudge factor"
((8*7000)*1000*1000)/450500=124,320ft-lb

an online physics calculator comes up with the same result as the convoluted formula that converts to grains.

so why is my simple version of the calculation off by a factor of 32?.... or is it? i don't see what's going on here.

 

[More Coffee]

have a look and see that the velocity every one is using is also in feet and not in meters

Oldly your factor of 32 is also somewhat found in that there is 3.2 feet/meter

 

[Ian Rogers]

I get 167.642k.... I think the formula is for metric mass = 3.628 kg velocity = 304 m/s

 

[crutschow]

It's not commonly used but the unit of mass in English units is slugs which is pounds divided by ≈32 (the acceleration of gravity). So there's your observed difference of 32.

Pound is a unit of force not mass.

 

[squishy36]

Learn to use the GNU units program (one of the most heavily-used programs on my computer) and you can do such calculations easily and without mistakes:

You have: 0.5 8 lbm (1000 ft/s)^2
You want: ft lbf
        .5 8 lbm (1000 ft/s)^2 = 124324 ft lbf

The real motivation is that it handles virtually every unit you'll come across and it tells you if you make a dimensional error. Even though I learned to do these calculations before computers (and, thus, I can do them correctly on paper), it's much faster to use the GNU units program -- it's an excellent tool that should be in every technical worker's toolkit.

For the electrical guys, it is quite useful in helping convert between gaussian and rationalized MKS or SI units -- something you often have to do when using old materials.

 

[duffy]

I converted to metric and got 168,572 J, which equals 124,332 ft-lb.

Looks like crutschow found the problem: slugs = m, lb = m x a.

Slugs, feet, and barelycorns - ugh! Use metric when you are doing science.

 

[JimB]

I cannot explain it fully in imperial units (which just blew my mind at college over 40 years ago) but you are missing "g" the acceleration due to gravity.

In imperial units g is 32 ft/s².

I think the confusion comes in that 8lb is the weight, which is not the same as the mass.

Weight is a force (Mass x Acceleration), so the mass is 8/32, and what the units of that are is lost in the mists of time. (In the remains of my brain spread across the floor of Rugby College of Engineering Technology).

In SI units Mass is in Kilograms, and Force is in Newtons.
An object with a mass of 8kg has a weight for of 8x9.81 Newtons.

So back to your problem:

Mass = 8/32
V = 1000

Energy = 1/2 x 8/32 x 1000 x 1000 = 125000 ft.lb

JimB

 

[JimB]

Use metric when you are doing science.

I could not agree more!

JimB

 

[unclejed613]

Murphy's first corollary for math calculations is that if your inputs and outputs are in the same units, don't double-convert........

the online calculator output was in ft-lb, with inputs in ft/s and lb

my co-worker's inputs were in ft/s, and mass converted to grains (7000gr per lb) and divided by the "fudge factor" of 450500. his calculation agreed with the output of the online calculator. the energy formula is simple: E=m*v²*½.
i come up with 4 million. 8*1000²*0.5



EDIT: ok, i think i get it....but shouldn't the result be in ft-slugs?

 

[unclejed613]

ft-lb is the correct unit, for muzzle energy. i was trying to figure out how much energy in the "mythbusters-mishap" projectile. an 8lb cannonball traveling 1000ft/s.

 

[BrownOut]

EDIT: ok, i think i get it....but shouldn't the result be in ft-slugs?

Let's look at the dimentions. E=1/2*m*v^2. We can re-write: E=1/2*(m*d/s^2)*d. The quantity in parenthesis is (mass(slugs)*acceleration(feet^2/s)) or lbs (if scaled appropriately) and so the dimentions we are left with is foot*lbs.

 

[lebevti]

use SI units and then get back to us

 

[BrownOut]

No thanks. I'm perfectly comfortable with the units I've used.

 

[lebevti]

i know u are, but most people arent...SI is the standard and it's hard for people to help you when they have to convert ur nits into the standard

we are taught the standard in school and thats what we go by

 

[duffy]

We were taught both SI units and how to write legibly.

 

[BrownOut]

Were you also taught how to ask for help? This is not the way.

use SI units and then get back to us

I don't respond to demands.

 

[lebevti]

not a demand...just a suggestion

 

[Ratchit]

unclejed613,

Sorry I am so late in answering this, but I was on vacation.

so why is my simple version of the calculation off by a factor of 32?.... or is it? i don't see what's going on here.

It is off, and here is why. A slug is the mass that 1 pound of force will accelerate at 1 foot/sec^2. If 32 lbs of force are applied to a slug, then it will accelerate proportionately at 32 ft/sec^2 . So if you know how many slugs and the velocity, you can easily calculate the ft-lbs of energy. And, of course, you can determine how many slugs by dividing the lbs of force at Earth gravity by 32.

EDIT: ok, i think i get it....but shouldn't the result be in ft-slugs?

No, the slugs (mass) get converted into force (lbs) by the acceleration needed to bring the mass up to the designated velocity.

Ratch

 

[KeepItSimpleStupid]

It's that goofy thing where you as a person weigh a different weight on the moon than Earth, but you have equal mass on the moon and the Earth.
Same is, of course, relative because the acceleration due to gravity varies slightly too. See: https://en.wikipedia.org/wiki/Gravity_of_Earth

Slugs used to be the things you find hiding in the back yard and kill with beer.

 

[Ratchit]

KISS,

It's that goofy thing where you as a person weigh a different weight on the moon than Earth, but you have equal mass on the moon and the Earth.

Nothing goofy about it. Weight is the keyword. Weight is the measure of induced force on a mass by a designated gravity, which in turn is measured by the acceleration it causes.

Ratch