Calculating Density: A Challenge for Aviation Maintenance Students

[AMTSOUTH]

My teacher gave us a problem to find the density of an object that weighs 40 lbs. and has a volume of 120 cubic inches. I think the answer is .33 lbs. per cubic inch, my teacher said it is 3.3 and some of my classmates said it was something way different. In my teachers defense he is a mechanic, not a physicist, trying to teach an Aviation Maintenance Tech. program. He gets a lot of stuff wrong and the students have to keep correcting him, but he could fix anything on an aircraft. Please help me and explain the your process! Thank you!

 

[Doc Al]

I'd say you were correct. There's not much to it: Weight/Volume, both of which are given.

Ask your teacher to explain his answer and show his calculation.

 

[AMTSOUTH]

Thank you!

 

[Emilyjoint]

Density is mass/volume and if you were using SI units it would be mass in kg/volume in m^3
not weight in Newtons/volume

 

[D H]

Density is mass/volume and if you were using SI units it would be mass in kg/volume in m^3
not weight in Newtons/volume

The OP is not using SI units.

In English units, pounds without a qualifier is a unit of mass. Pounds force is a unit of force.

 

[tms]

In English units, pounds without a qualifier is a unit of mass. Pounds force is a unit of force.

Last time I checked, the slug was the unit of mass.

 

[D H]

One pound: http://www.google.com/search?client=safari&rls=en&q=one+pound&ie=UTF-8&oe=UTF-8
That's the pound avoirdupois that Google uses, which is a unit of mass.

That is also the default meaning of a pound at wolfram alpha: http://www.wolframalpha.com/input/?i=one+pound

Most importantly, this is what the term "pound" sans any qualifiers means per the National Institute of Standards and Technology.

 

[Emilyjoint]

but density definately = mass/volume not weight/volume ?

 

[Doc Al]

but density definately = mass/volume not weight/volume ?

Some people use weight density, which is weight/volume. Given the context, that's what I presumed. (But pound mass would also work.)

But you're right, density usually means mass/volume.

 

[Emilyjoint]

I have never met density given in Newtons/m^3 and I would lose marks if I wrote density = weight/volume.
I would love to know who, in physics, uses weight density. Who teaches that !

 

[D H]

I have never met density given in Newtons/m^3 and I would lose marks if I wrote density = weight/volume.
I would love to know who, in physics, uses weight density. Who teaches that !

Without any qualifier on the word "pound", a pound is unit of mass, not force. Pounds per cubic inch is a density.

Perhaps you are thinking of the pound force. Some people use pound without a qualifier as a force. This is erroneous. This is somewhat okay when it is obvious that the quantity in question is a force. For example, pressure in pounds per square inch. This is better written as pounds force per square inch (or just use psi, which is short for pounds force per square inch).

 

[Doc Al]

I would love to know who, in physics, uses weight density. Who teaches that !

It's a crazy world out there!

 

[tms]

The present problem says the 40 pounds are a weight, and weight is a force.

 

[skeptic2]

Is the distinction between mass and weight commonly made in metric countries?

I asked my brother in law who used to teach science at the middle school level in Mexico, how he would express the weight of an astronaut walking on the moon. Would he say he has 1/6 his weight on Earth in kilos or in Newtons. He replied "in kilos" and didn't even know what Newtons were.

Is this common in other metric countries?

 

[Emilyjoint]

I have just looke on the beloved Wiki...In the US oil and gas industry weight density is sometimes used.
It certainly is a crazy world. I am worried enough about physics lessons and 'help'

 

[Doc Al]

Perhaps you are thinking of the pound force. Some people use pound without a qualifier as a force. This is erroneous.

Just to nitpick (though I defer to your opinion on the matter): Back in the day, in some elementary physics classes, rightly or wrongly an unqualified 'pound' always meant a force and the corresponding unit of mass was the slug. (Perhaps this was just 'understood' in the context of that textbook/class.)

Edit:
Ah... I happen to have my trusty Halliday & Resnick (1966) right here:

"Legally the pound is a unit of mass but in engineering practice the pound is treated as a unit of force or weight"

"In this book only forces will be measured in pounds. Thus the corresponding unit of mass is the slug."

 

[D H]

The present problem says the 40 pounds are a weight, and weight is a force.

You are reading too much into the term "weighs" ("an object that weighs 40 lbs.") . Weight, particularly in English units, is often a synonym for mass -- unless the quantity in question is a force.

That weight in pounds force and mass in pounds mass are more or less numerically equal is at times rather convenient for problems here on the Earth.

 

[Emilyjoint]

does that textbook say that density = weight/volume?

 

[Doc Al]

does that textbook say that density = weight/volume?

That would be atypical in a physics text, but engineering is another story!

 

[D H]

Edit:
Ah... I happen to have my trusty Halliday & Resnick (1966) right here:

"Legally the pound is a unit of mass but in engineering practice the pound is treated as a unit of force or weight"

In practice, some engineers who insist on using English units use pounds mass for mass, others use slugs. (The poundal as a unit of force is pretty much dead, fortunately.) Some of those engineers who use pounds mass and pounds force are nicely explicit and use lbm and lbf. Others leave it up to the reader to determine whether that "lb" in their spec document is a unit of mass or force. It's a mess.

 

[Emilyjoint]

My dad did physics in the 60s and he tells me that pounds, slugs and poundals were a mystery.
He tells me that sometimes to get the right answer 'you had to multiply by 32'... something to do with mass and weight and feet per second.
Wikki says that force is poundals.
good night !

 

[tms]

You are reading too much into the term "weighs" ("an object that weighs 40 lbs.") . Weight, particularly in English units, is often a synonym for mass -- unless the quantity in question is a force.

That's just sloppiness, caused in part by the fact that the English verb `weighs' is so convenient, whereas `masses' is rather ugly.

That weight in pounds force and mass in pounds mass are more or less numerically equal is at times rather convenient for problems here on the Earth.

They are numerically equal only here on Earth. Or wherever $g$ is the same by coincidence.

 

[skeptic2]

Most likely there was no distinction at all between mass and weight before Isaac Newton and the languages haven't evolved to keep up with science.

My dictionary doesn't recognize a verb, to mass, meaning to determine the mass of an object.

 

[tms]

My dictionary doesn't recognize a verb, to mass, meaning to determine the mass of an object.

This is English. We can verb nouns whenever we want to. As Calvin said to Hobbes, "Verbing weirds language" (or words to that effect).