Comparing Mass and Weight: Sample A vs. Sample B

[scava]

1. Two samples are weighed under identical conditions in a laboratory. Sample A weighs 1 lb and Sample B weighs 2 lb. Does Sample B have twice mass of Sample A? Why or why not?

Homework Equations

The Attempt at a Solution

I said that no, it would not be because mass and weight are different. Mass is the amount of 'stuff' that is in an object, weheras weight is the amount of gravity exerted on an object...but I don't think this is complete enough?

 

[D H]

Before I help:

(1) Was this a quiz/test that you are just trying to get confirmation on regarding your answer, or is it an ongoing homework problem to which your initial answer is "no"?

(2) What are the relevant concepts? What makes you think that the mass of sample B is something other than twice the mass of sample A?

 

[scava]

It was actually just a discussion question, so I was just curious what the 'correct' answer was...It was sort of thrown out there and I just didn't feel I had a complete enough understanding of it..

I was thinking that the mass would be different because of the weight factor of lbs. Mass is measured with a balance and weight is measured with a scale...I guess I am just not putting 2 & 2 together here...

 

[scava]

I understand that the mass would be the same on Earth or on the moon, whereas the weight would be only 1/6 on the moon because of the difference in gravitational force, but comparing the two by pounds...in the same lab under exact same conditions...I would think that 2 lbs WOULD BE twice the mass as 1lb, because the same amount of gravity is weighing on both and mass doesn't change ...geez, I just am not sure why I don't get this concept...

 

[D H]

No matter how you measure or define weight, and no matter how you define pounds, the answer is "yes".

There are two different kinds of scales. A balance scale measures mass. If a balance scale was used to measure the samples, the answer is obviously yes. A spring scale measures "apparent weight", and "under identical conditions in a laboratory", the apparent weight is proportional to mass. If sample A has some apparent weight and sample B has twice that apparent weight, the answer to the question is still yes because the ratio of the weight of sample B to the weight of sample A is exactly equal to the ratio of the masses.

There are two different pounds. A pound-mass (lbm for short, or just lb) is a unit of mass. A pound-force (lbf for short, and never lb) is a unit of force. Since you said lb, I assume you are talking about pounds-mass. If you are talking about pounds-force it is always a good idea to never, ever use lb to indicate the units.

There are three different definitions of weight. Legally, weight is mass. It would vex the commercial world considerably if the contents of a one pound can of peas weighed something other than one pound anywhere on the Earth, or on the Moon, for that matter. Lawyers and merchants don't give a hoot about what physicists think, but they do care a lot about things that don't measure up.

"Apparent weight" is what a spring scale measures. The apparent weight of some object is the sum of all forces acting on the object except for gravity. The apparent weight (measured in pounds-force) of the contents of a one pound (one pound mass) can of peas varies from place to place on the Earth. It weighs a bit more than 1 lbf in Nome, Alaska, and a bit less than 1 lbf at the top of Mount Kilomanjaro. The apparent weight on the surface of the Moon: about 1/6 lbf. The apparent weight on the International Space Station: very close to zero.

"Actual weight", or just plain weight, is the mass of the object times the acceleration due to gravity. The actual weight of a one pound can of peas also varies a bit from place to place on the Earth, but not as much as does apparent weight. The actual weight on the surface of the Moon: about 1/6 lbf. The actual weight on the ISS: about 0.90 lbf.

Fortunately, you don't have to worry about actual weight here because neither a balance scale nor a spring scale measures actual weight. What measures actual weight? Nothing. There is no way to measure actual weight.

 

[scava]

Wow...that is very clear..I get it..I wish you were my chemistry instructor ! Thank you very much for clarifying this! ~ Now it makes perfect sense...

 

[Borek]

Answer doesn't have to be yes. If both objects have different density and are weighted in the air, you should account for the air buoyancy. Differences are small, but perfectly measurable using analytical balance.

 

[D H]

Since I am not associated in any form with Google, I have no qualms in saying their calculator is amongst the best in understanding the difference between pounds and pounds-force. Some examples:
http://www.google.com/search?q=1+pound+in+kilograms"
http://www.google.com/search?q=1+pound-force+in+Newtons"
http://www.google.com/search?q=1+pound-force+/+1+pound"
I forgive them that last answer. For some unexplainable reason the Google calculator really likes the metric system.

I have two kids in college and am still recovering from one who just graduated. Enough to drive one to drinking. Let's see. If I drink a firkin of beer every other week, what does that mean in terms of metric units?
http://www.google.com/search?q=1+firkin+/+fortnight"
What kind of silly answer is that?
http://www.google.com/search?q=1+firkin+/+fortnight+in+liters+/+day"
Oh. 1 firkin/fortnight = liver damage. I better not do that then.