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Windseaker
4000lb of water are at the top of a 200ft. waterfall ready to fall. What is the amount of gravitational potential energy?

PE = mgh, F = ma, F = mg, Therefore gravitational PE = Fh

PE = Fh

PE = (4000lb)(200ft)
=800,000lb(ft) ?

is this right?

if so can you help me understand Kinetic Energy of this problem (then water hits) as well??
Guest
QUOTE (Windseaker+Apr 17 2010, 05:53 AM)
4000lb of water are at the top of a 200ft. waterfall ready to fall. What is the amount of gravitational potential energy?



blink.gif ...... lb & ft laugh.gif - try converting to SI units (kg & m) and you'll @ least be on the right starting blocks.

smile.gif
Matador
4000lb of water is a mass and needs to be converted into a Force so that PE=mgh still applies. cool.gif

For the second part, assuming no loss due to friction, PE at the top = KE at the bottom.

cool.gif
NoCleverName
A bit of a change, here, Matador.

The 4000 lbs is not a mass, it is a force since the acceleration due to gravity is built into "pounds". So, Windy, you were on the right track to multiply by simply feet (the "h"). I think the resulting English unit is the "foot pound".

You could, if you desire, make the necessary conversions to joules (divide the pounds by 2.2, the feet by 0.3048, stick in the acceleration of gravity 9.8).

As far as the sarcasm coming from "guest" is concerned ... the choice of a system of units does not change the basic physics of a problem ... although is might make the results more compatible to other uses.
Matador
QUOTE
A bit of a change, here, Matador.

The 4000 lbs is not a mass, it is a force since the acceleration due to gravity is built into "pounds". So, Windy, you were on the right track to multiply by simply feet (the "h"). I think the resulting English unit is the "foot pound".

You could, if you desire, make the necessary conversions to joules (divide the pounds by 2.2, the feet by 0.3048, stick in the acceleration of gravity 9.8).






Lb can be converted to Kg.

Kg is the standard unit of mass.


Therefore, 4000lb of water, is the mass of the water.


huh.gif
NoCleverName
QUOTE (Matador+Apr 17 2010, 06:56 AM)
Therefore, 4000lb of water, is the mass of the water.


Nah, the pound is a unit of force ... which is what your bathroom scale measures. You are applying a force in pounds against the measuring spring. No different than if you put the scale up against a wall and pushed on it to create a given force in pounds.

Yes, there is a "conversion", valid only at the earth's surface.

So Windy was properly seeing the "trick" in the problem.
Matador


http://en.wikipedia.org/wiki/Mass

QUOTE
On the surface of the Earth, the weight W of an object is related to its mass m by W=mg where g is the acceleration due to the Earth's gravity, equal to about 9.81 m s−2. An object's weight depends on its environment, while its mass does not: an object with a mass of 50 kilograms weighs 491 newtons on the surface of the Earth; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons.

In the International System of Units (SI), mass is measured in kilograms (kg). The gram (g) is 1⁄1000 of a kilogram.


4000lb = ~ 1818kg. so the mass is 1818kg.

SO the PE = mgh

Sorry am I not understanding something here?
Matador
QUOTE
You could, if you desire, make the necessary conversions to joules (divide the pounds by 2.2, the feet by 0.3048, stick in the acceleration of gravity 9.8).


You've already stated exactly what im saying.

PE = (4000/2.2)x9.81xheight


blink.gif blink.gif
Windseaker
I believe this is right. except---ft*lbs

PE = mgh, F = ma, F = mg, Therefore gravitational PE = Fh

PE = Fh

PE = (4000lb)(200ft)
=800,000lb(ft) ?---------------800,000ft*lbs.

ft*lbs is a English unit for Energy and does not need to be converted to joules!

The KE=PE(when water is at the bottom or impact)!

English units are important too, unfortunately, but very real.

Anyone what to double check me here? mellow.gif
Plumb Bob
QUOTE (Windseaker+Apr 17 2010, 05:09 PM)


PE = mgh, F = ma, F = mg, Therefore gravitational PE = Fh

PE = Fh


English units are important too, unfortunately, but very real.

Anyone what to double check me here?  mellow.gif

Windseaker.
You can use the Eng system of units if you prefer, but I find that using force in "pounds" can become ambiguous under some (many) circumstances, and even confusing.

To exemplify, let me ask you a quest.

You like to say: PE = mgh, and F = mg = W, thus for English, F is given in 'pounds', correct?
So let me ask you; since you derived force from F = mg, then what units (in English system) is the mass, m, given in ??

Bob
NoCleverName
QUOTE (Plumb Bob+Apr 18 2010, 03:25 PM)
then what units (in English system) is the mass, m, given in ??


Slugs
Plumb Bob
QUOTE (NoCleverName+Apr 19 2010, 12:44 AM)
Slugs


Exactly; and when in the last 30 years have you heard anybody refer to gravitational mass in terms of so many "slugs" ?(sounds like a boxing match laugh.gif


The truth is most people today trying to use the English system end up referring to both the force and the mass in terms of "pounds" . But then the reader is left to guess whether they are referring to mass or weight. So, unless it is specified, we have this pound-force / pound-mass confusion.
This link mentions it somewhat under the "foot-pound-second" sub-title.
http://physics.info/system-english/

Tcr
In his original question, the poster states that 4000lb of water was used, not 4000lbf (pounds force) was used. Therefore the 4000lb refers to mass, not weight.
Windseaker
Ambiguous is an understatement!
Here in the us, it is very ambiguous to live in two worlds English & SI
Lbs, ft*lbs, slugs are used as well as btus and how about a lb*ft!
Mass, force, weight

The US world of units is vast, abroad you imports are already SI units.

Still, you never know what you boss my ask.

try this, what SI unit is mass? is it really kgs? huh.gif
Plumb Bob
QUOTE (Windseaker+Apr 19 2010, 05:31 AM)
Ambiguous is an understatement!
Here in the us, it is very ambiguous to live in two worlds English & SI.


The US world of units is vast, abroad you imports are already SI units.

Still, you never know what you boss my ask.



I'm glad you recognize it, Windseaker. But don't take it so hard. At least you didn't loose a $ 125 million dollar satellite over it.
Read all about it: http://www.cnn.com/TECH/space/9909/30/mars.metric.02/

That's right. A 125 MILLION DOLLAR Martian Satellite crash over this very thing, English / metric conversion.
Oh, By the Way; in today's currency that's 82 million POUNDS. laugh.gif
Hey! Its only MONEY, right? laugh.gif

.
NoCleverName
"Pounds" is not, and never will be, a unit of mass. Now, conventionally we consider it to be a "mass-like" measure here on the planet's surface. There's no real harm in that until we need to do physics computations.

You should consider that on a different planet's surface, an object's weight in pounds will be different from that here on earth. On the other hand, it's mass in kg will be the same.

This is so elementary I'm wondering if I'm sounding pedantic.
Lunarlanding
QUOTE (Plumb Bob+Apr 19 2010, 02:55 PM)


Read all about it:  http://www.cnn.com/TECH/space/9909/30/mars.metric.02/

That's right.  A 125 MILLION DOLLAR Martian Satellite crash over this very thing, English / metric conversion.
Oh, By the Way; in today's currency that's 82 million POUNDSlaugh.gif
Hey! Its only MONEY, right? laugh.gif

.



Very funny, Bob.
I guess you could say.... a Martian satellite launched from earth weighing about 1400 pounds eventually reaches Mars and looses 82 million pounds. biggrin.gif

Hmmm.
Plumb Bob
QUOTE (Lunarlanding+Apr 20 2010, 06:09 AM)


Very funny, Bob.
I guess you could say.... a Martian satellite launched from earth weighing about 1400 pounds eventually reaches Mars and looses 82 million pounds. biggrin.gif

Hmmm.


That's about the bloody size of it. Penny wise and POUND foolish if ya ask me, mate. rolleyes.gif
Maybe they should save $ by shutting down that welfare agency for the intelligencia called LIGO. biggrin.gif Results have failed to produce a thing.
Joe

Lunarlanding
QUOTE (Plumb Bob+Apr 21 2010, 02:55 PM)


Maybe they should save $ by shutting down that welfare agency for the intelligentsia called LIGO. biggrin.gif


You probably meant to say the government welfare agency called public University tenure for professors. laugh.gif

QUOTE

(LIGO) results have failed to produce a thing.


Sure it did.... it produced "NULL results". biggrin.gif
And think about all the non-governmental industry that benefited... like the private industry concrete manufacturer who had to fabricate miles of concrete tunnels... http://upload.wikimedia.org/wikipedia/comm...Reservation.JPG
...and all the new buildings that had to be designed and constructed by hardworking hard hats getting paid over-time.... ..and all the asphalt roads that needed to be constructed to reach these sites:(isn't it worth a few hundred mil dollars just to upset the environMENTAL wachos?)
http://atlasobscura.com/place/ligo-livingston-observatory
http://www.ligo.org/multimedia/gallery/lho...ges/Aerial4.jpg
....and all the extra Terra-bytes of hard drives that had to be purchased to crunch all the data runs.
....and just think about all the Domino Pizza delivery guys that got extra tips for delivering free pizzas (exceeding the 30 minute guarantee) to all those dead heads out there in nowhere-ville miles from grocery stores ... http://www.ligo.org/multimedia/gallery/lho...ges/Aerial5.jpg

See; isn't federal government socialism wonderful? laugh.gif

Lunar
Matador
Can somebody please clear this up? A couple of posters have stated that 'pound' is a measure of force, and that it has gravity already 'built' into it.

As far as i can see, the pound in the original question referred to mass as otherwise the unit of lbf would have been used.

Reading the wiki entry on 'pound'

http://en.wikipedia.org/wiki/Pound_(mass)

QUOTE
The pound or pound-mass (abbreviation: lb, lbm) is a unit of mass used in the imperial, United States customary and other systems of measurement. A number of different definitions have been used, the most common today being the international avoirdupois pound of exactly 0.45359237 kilograms.



huh.gif
NoCleverName
QUOTE (Matador+Apr 22 2010, 12:24 AM)
Can somebody please clear this up? A couple of posters have stated that 'pound' is a measure of force, and that it has gravity already 'built' into it.


You don't measure a rocket engine's reaction force in kilograms do you? You'll hear it referred to as pounds of thrust. In SI units it's the newton.

You'll often hear that someone weighing "180 pounds" on earth will weigh but "30 pounds" on the moon. You don't hear about them losing 70 or so kilos, though, do you?

I can't help it that sloppy terminology has entered common language.

In the OP a weight of "4000 pounds" was mentioned and you had to calculate a potential energy PE=mgh. Now, if the problem mentioned a mass of 1800kg then you would immediately multiplied by 9.8m/s^2 to handle the "mg" term. But in "pounds", would you have multiplied by 32fps^2 to handle "mg" (staying in english units)? No.

Observe you suggested dividing by 2.2 and then multiplying by 9.8. But what were the units of that "2.2"? They were "pounds per kg". And if you carefully backtrack the units of PE=mgh using the conversion factor you will find that "pounds" aren't really a unit of mass since there's an acceleration built in.

Start with
CODE
lb*ft = M*g*h


on the right substitute g=m*s^-2, h=m

on the left ft=c*m (conversion factor "c" feet per meter)

solve for lb and you get something in the form

lb = (M*m*s^-2)/c

which is essentially F = Ma
Limon
Yep: NoCleverName is correct.

A kilogram is a unit of mass, a newton is a units of force. The average gravitational force exerted upon (or by) a kilogram is 9.81 newtons on the Earth’s surface.

(4000 lb / 2.2) 1,818 kilograms is 17,835 newtons.

I believe Potential Energy is force (newtons) times distance (meters). A joule is a newton meter.

200 ft * .3048 = 60.96 meters

17,835 newtons * 60.96 meters = 1,087,222 joules

Now lets check our math. d = ½ v²/a, 60.96 meter = .5 * v * v / 9.81 m/sec/sec; or, 60.96 * 2 * 9.81 = v², or v = 34.58 m/sec

Ke = ½ m v² or .5 * 1818 kg * 34.58 m/sec * 34.58 m/sec =1,087,078 joules.

Looks like it is correct because PE before the fall is equal to Ke after the fall.

Now if you are going to use the English system you will have to become familiar with Slug (mass), pound (force) 32 ft/sec/sec (gravitational accelerate) and v in feet per sec.

But it is easier to just convert joules to foot pounds.
Limon
I found out something rather interesting.

Microsoft has a program called ‘convert’ that converts one unit into another unit (feet to meters; joules to pound-feet; liters to quarts etc). It is quite comprehensive. I was very surprised to see that Microsoft does not know what a slug is. Slug was not listed in the units of mass. Now I do not believe every thing I read, so I was not dismayed, but this little over sight was very interesting. And maybe warrant of a little thought.

4000 pounds at a height of 200 feet is 800,000 foot points of energy. PE = distance times force.

If an object is dropped 200 feet it will have a velocity of 113.44 feet per second. d = ½ * v² / a a = 32.17 ft/sec/sec, d is 200 ft

Ke = 1/2mv²: So this should be a true statement if pound is a mass. 800,000 ft-lbs = ½ * 4000 lb * 113.44 ft/sec * 113.44 ft/sec, but the product is much too high 25,737,267.

This proves that pound is not a mass. 25,737,267 / 800,000 = 32.17. The product needs to be divided by 32.17. Or 4000 / 32.17 = 124.34 slugs.

I am guessing that a slug has a mass that is equal to 32.17 pounds of force on the Earth surface. This happens to be the rate of gravitational acceleration (in feet per sec. per sec.) in the English system as 9.81 m/sec/sec is in the metric system. And the kilogram has a mass that is equal to 9.81 units of force (newtons) on the Earths surface.

It looks like Man set the meter as a unit of distance. He then set the cubit decimeter as a unit of volume. He set the cubit centimeter (of water) as a unit of mass. The unit of force necessary to accelerate one kilogram at a rate of one meter per second per second was called a newton. The gravitational force of the Earth exerts 9.81 such newtons of force upon one kilogram.

Something similar must have been done in the English system.

“From Diamond; Fundamental Concepts of Modern Physics” ‘One slug is the mass that will experience an acceleration of 1 ft/sec² when under the influence of an unbalanced force of one pound’.

But the scientific community (at least Microsoft) does not even know what a slug is. So it is probably time to drop the system.
NoCleverName
Got something right, Limon.

Now if we can just break you out of your nutty ideas about angular momentum. wink.gif
Limon
Angular momentum conservation does not work in the lab. And energy can be made from gravity. There are holes in physics that you can drive a bus through. I am building trebuchets using only a wheel. Moderate increases in velocity make large increases in distance. The wheel/trebuchet (as it opens) is not conserving energy it is conserving linear Newtonian momentum.
NoCleverName
QUOTE (Limon+Apr 27 2010, 08:26 PM)
Angular momentum conservation does not work in the lab. And energy can be made from gravity.

Yup, that's our ol' Limon! cool.gif
wwwnice
i have no idea about it, tady i am happy very much .

beause i brought very cheap products from http://www.homybuy.com

biggrin.gif
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