Physics Question (1 Viewer)

[Holadem]

I remember in geometry learning a formula. . .

height = 1/2gravity * time^2 + initial velocity * time + initial height

to show the relation of time and height of a falling object but this formula totally ignores that different objects have varying surface area to mass ratios and do in fact fall at different rates. I believe that it was Newton who said that all objects fall at the same rate. But, can you really compare the fall rate of an apple to a parachuter?

No kidding. There formulas are used with the assumption of point mass, which means that for the purpose of the experiment, all the mass of the object is considered to reside in a single point, the center of gravity. This eliminates many considerations of the real world, such as air resistance. That (and many other such simplifications) is the basis for these simple formulas. Any teacher worth his weight in donuts would have made that clear. Take your physics book, and I am ready to bet that point mass is defined and the assumption made before any of those formulas are thrown at you. If not, then throw the book away, along with your professor.

There is a reason this is called elementary physics.

Some revelations indeed...

--
Holadem

 

[Leila Dougan]

In addition to what everyone has said, the problem also lies with the fact that he's using a SCALE to measure the weight. If you calculated the weight based solely on mass and gravity, then this buoyency bit wouldn't play any part. Vaccuum or no vaccuum, the mathematically calculated weigh would remain the same as long as the gravity and mass remain the same.

 

[Cees Alons]

True.
Which leads me to this off-topic question: Someone told me that American food-recipe's are solely based on volumes, not weight. So you wouldn't have (or at least: need) a scale in the kitchen. Is that true? Do you only have a volume measuring device, probably having marks saying "sugar", "salt", "beans", and so on - or really based on volume only?
In a European kitchen (anyway, in a Dutch kitchen), the scale is one of the most essential attributes. (We measure liquids by volume, same for little quantities, like one theespoon of salt, two table-spoons of sugar, apples and the like by numbers, but e.g. the amount of flour or raisins is always given in grams or kilograms.)

Cees

 

[Julie K]

Cees,
For the most part dry goods (flour, sugar, etc) in US recipes are specified as volumes, usually as fractions of a 'cup' (1 cup = 236.6 ml).

I would guess that most Americans don't have scales in their kitchen. I have a few oddball recipes that specify the weight of the ingredients so I do have a scale. I also buy meat in bulk and then weigh it out in smaller amounts and freeze it.

I've read that many think weighing flour is more consistent than measuring a volume of flour, but most of these items, flour, beans, rice, are quite variable in how much liquid they'll absorb and so a certain amount of judgement is required in any case.

 

[Cees Alons]

Julie,

Thanks. It means one would have to convert recipes. Funny.

BTW, a "cup" is almost proverbial here for the amount you will try to borrow from your good neighbour if you would run out of, say, sugar when shops are closed. In fact I think it hardly ever happens - not more frequently than someone slipping on a banana peel in real life.

Cees

 

[andrew markworthy]

Just a minute - since at the start it was stated that a pound of feathers weighs less than a pound of nails, then surely you know the correct weights before you begin the problem? Therefore, surely the problem implicitly recognises that the error is in the measurement rather than a genuine intrinsic difference?

 

[Leila Dougan]

Andrew, exactly! Which is why the problem is nothing more than proof that scales are only for convenience and that they are not accurate for determining actual weight.

 

[Chris Farmer]

Atually, Lella, they're fine for determining weight, since weight is nothing more then a force. What they're useless for is determining MASS.

 

[Julie K]

Yeah, but just think how gross cookbooks would be if they specified mass in British units...

"Add 2 slugs of flour and mix well"

 

[Rob Gardiner]

Leila,

Andrew, exactly! Which is why the problem is nothing more than proof that scales are only for convenience and that they are not accurate for determining actual weight.

Not quite. Chris Farmer has it right. There is still some confustion on this thread about the difference between weight and mass. There is no difference between "actual" weight and the weight as measured by a scale. What a scale measures IS the actual weight.

What the problem demonstrates it that two object with the same weight can have different mass, due to buoyancy.

It also demonstrates that the formula Weight = Mass x Gravity is not the whole story since it does not take buoyancy into account.

 

[Lew Crippen]

Thanks. It means one would have to convert recipes. Funny.

And sometimes the conversion is a two-step process: metric to English and then weight to volume. Actually I have a book with weight (in grams) to volume (in cups/tablespoons/teaspoons) equivalents for some different, common cooking ingredients such as sugar and flour.

This is not at all a problem for liquid measure of course—only dry ingredients.

 

[Julie K]

It also demonstrates that the formula Weight = Mass x Gravity is not the whole story since it does not take buoyancy into account.

It's Force = Mass * Acceleration. Keep track of all your forces, including buoyancy, and all your accelerations and you do get the whole story.

 

[StephenK]

Yeah, but just think how gross cookbooks would be if they specified mass in British units...

"Add 2 slugs of flour and mix well"

or in my case...take 2 stone of sugar and 1 stone of butter...

Since I'm such a huge honking pig!

 

[Hunter P]

Thanks for the laugh. Especially the last quote. My whole world is now shattered.

The answer to your question was posed many times in this thread but you shot them down every time. If you still believe this was not a question of standards then maybe you need to rethink what is the definition of the term "standards."

 

[Lew Crippen]

I have a recipe that calls for weighing eggs.

Would that include the weight of the shell?

 

[Julie K]

Would that include the weight of the shell?

Actually, it does

Sometimes it's a real hassle sorting through a carton of eggs to get ones I can use.

I'm tempted to just weigh a few egg shells, determine an average, then weigh just the liquid part so I can use fractions of an egg.

 

[Holadem]

It's Force = Mass * Acceleration. Keep track of all your forces, including buoyancy, and all your accelerations and you do get the whole story.

Exactly. The very first thing you do in analysing a system is an ID of all the significant forces involved, depending of the degree of accuracy you wish to attain.

--
Holadem

 

[Leila Dougan]

Rob,

Not quite. Chris Farmer has it right. There is still some confustion on this thread about the difference between weight and mass. There is no difference between "actual" weight and the weight as measured by a scale. What a scale measures IS the actual weight.

I understand the difference between mass and weight. Weight = mass * gravity. Buoyancy isn't calculated into gravity, so a scale isn't accurate for determining weight of all objects. If the object has very little buoyancy then the difference is negligable and the scale's result is acceptable. However, when weighing feathers, the difference is too great and a scale is not a good way to measure it's weight. In that case, you'll need to calculate buoyancy (and other forces) to get a more accurate measurement.

Julie and Holadem said exactly what I meant to say, they just did a better job.

 

[Bill Catherall]

Hold on! The assumption that feathers are more buoyant than nails is false, or at least a bad assumption to make. Why does this teacher assume feathers to be more buoyant? Because they fall at a slower rate? That has nothing to do with buoyancy, it's terminal velocity, which is a relationship between the mass and the surface area. (That's why the apple falls faster than a parachuter.)

Buoyancy is a relationship between the density of the object and the density of the fluid the object is submersed in. An upward buoyant force is experienced when the density of the object is less than the density of the fluid.

So, given that all objects are at rest, the nails and the feathers, buoyancy is not an applicable force. Equilibrium has been reached. A pound of feathers in air will have the same mass as a pound of feathers in a vacuum.

 

[DaveGTP]

So, given that all objects are at rest, the nails and the feathers, buoyancy is not an applicable force. Equilibrium has been reached. A pound of feathers in air will have the same mass as a pound of feathers in a vacuum

Bill is right--that would be my understanding as well. Bouyancy is normally associated with liquids because we don't have very many things with lighter-than-air density. Weighing a helium balloon would be problematic because of bouyancy (helium is lighter than air), but feathers at rest should not have any bouyancy. If there was bouyancy, the feathers would float upward, of their own accord, even in totally still air (like a balloon). This of course does not happen.

Feathers will fall at a different rate, but that is due to air resistance. I think I am right in maintaining that a feather's air resistance at REST should make 0 difference in the weight.