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I am an 8th grade science teacher and I have the following question: How do we measure true mass on Earth? I teach that a balance measures mass, but I find that a spring scale gives the same answer. If, on Earth, a 100 g object weights approximately 1 N, it's mass should be 100 g on a balance, but not a spring scale. Yet I get 100 g on the spring scale as well. I have not found an answer to my quandary so perhaps I am not asking the correct question. Thanks for your help.
Question Date: 2004-04-23
Answer 1:

A balance measures mass by comparing the unknown to a standard mass...like a 1 kg gold standard... a spring scale, on the other hand, DEPENDS on the local value of G.

So a spring scale on EARTH IS CALIBRATED to give the same as the balance on EARTH...i.e. when the spring is stretched so far, the mass is 1 kg. But if you now take this spring scale to the MOON and use it, you will see that the 1 kg mass shows up at a weight which is UNLIKE (less) than the value on Earth. But if you took your balance with you, you would still get the same value for the mass.

So a balance is independent of the planet because you compare an unknown to a STANDARD mass. But a spring scale depends on the local gravitational field.

I hope this helps.

Answer 2:

You are asking a fine question. The weighing devices are all either calibrated to read mass on earth or to measure force. I have a couple of spring scales that read in Newtons. Yours is obviously calibrated to read mass, so it would give you the wrong answer in a place where the force of gravity was different. You are a good observer - I used to be amused and a bit annoyed when I sorted the science materials at IV School. There were a bunch of boxes labeled 'spring balances,' and it seemed to me they should be labeled 'spring scales,' since they were clearly not balances.

Answer 3:

Mass is a fundamental quality of an object that does not change, and is measured in grams and kilograms (or ounces and pounds if you are in the US). Weight is mass times gravitational acceleration, which actually makes weight a measure of force. If you wanted to be technical, something with a mass of 100 grams should have a weight (or force) of 100 grams times 9.80665 meters per square second (gravitational acceleration), giving you 980.665 gram-meters per square second.

Here's the tricky part: we don't measure weight this way. Instead we define the Earth's gravitational acceleration as 1 "Gee" (creating a new unit) and measure weight in kilograms of force or pounds of force, which is a kilogram or pound multiplied by 1 "Gee". This operational definition makes mass and weight equal in number, though not in units. People don't get the units right, so they tend to confuse mass and weight, saying "I weight 130 pounds" and not "I weigh 130 pounds of force". Chances are, your spring scale doesn't say 100 grams of force just 100 grams.

If you were to take your 100 gram object to a planet where gravitational acceleration was only half that of the Earth's (one-half Gee), the mass would still be 100 grams measured on the balance, but the weight would no longer be 100 grams of force on the scale.

What would it be now?

Answer 4:

It depends on how the spring scale is calibrated. I have seen spring scales calibrated in grams, Newtons, or even old ones in ounces. If you want a spring scale that is calibrated in Newtons, you can probably order one through any of the science product catalogs.
Now, I'm not sure if you are asking about calibrating spring scales, or if you are really asking about the fundamental difference between mass and weight.
On Earth, any device that uses the gravitational field of the earth in making the measurement is really measuring WEIGHT, so both your measuring devices are actually measuring weight, even though they are calibrated in grams. But, if your scales are calibrated correctly, you are also measuring their true mass; you are just using the gravitational field of the earth to do so.
Mass we define loosely as the quantity of matter in a given object, which is really saying how many atoms are in a given chunk of "stuff", and what are the atomic masses of these atoms. Weight is a measure of how that mass behaves in a gravitational field. We define weight as "mass x g" where "g" is the acceleration of a freely falling object near the surface of the earth, for which the air resistance is so small as to be negligible.
The value of g is approximately 9.8 meters/second/second, using the metric system. So, 1 kg of mass has a weight of 9.8 Newtons, or approximately 10 Newtons. 100 gr = 0.1 kg, so it has a weight of 0.98 Newtons, or approximately 1 Newton.
Conversely, we define a Newton as the force that you would have to apply to a 1 kilogram mass to give it an acceleration of 1 meter/second/second. If you apply 9.8 Newtons of force to a 1 kilogram object, it will have an acceleration of 9.8 m/sec^2, and if you drop a 1-kg object on earth, it will also have an acceleration of 9.8 m/sec^2. We call this an acceleration of "1g". That's pretty fast. Just to make sense out of this, if you have ever been on the "Scrambler" at Magic Mountain - it has a horizontal acceleration of about 1g. I once tried to measure it with a mass and a spring scale!
You have hit, actually, upon one of Einstein's fundamental questions! Why should two objects have the same mass when measured in two different ways, by accelerating them horizontally (independently of gravity) and vertically, using gravity? So he defined gravitational mass and inertial mass, and one of his fundamental postulates is that gravitational and inertial mass are equivalent. Give a student two different objects and ask her to tell you which one is heavier, and then observe what she does. She'll move them up and down in each hand. The mass that offers greater resistance to beingmoved up and down or side to side has more "inertial mass". The one with more mass will weigh more on a scale, too. We call this way of measuring mass "gravitational mass", that is, the resistance to being pulled "down" by the mass of the earth.
Ok, so "everyone" knows that if you go to the Moon you weigh less, and if you go to Jupiter you weigh more. But, what if you go into orbit? You appear to be weightless, but you have not lost any mass! So how can you measure mass in free fall, as you are in orbit? (You are not really weightless, as "g" is about 70% of g on earth, so you don't actually weigh that much less. You only feel weightless because the shuttle is also in orbit, and everything is in orbit, and so the floor is falling as fast as you are, so you can't stand on it!)
What do you do? You would use the same principle you used to compare the inertial masses of two objects on earth: you would shake it! Really, that's what they do. They use an "inertial balance". They put an object in a pan balance, but instead of moving up and down in a gravitational field, the balance moves side to side, and has springs, and they TIME it. The smaller the mass, the faster it oscillates, and vice versa. The instrument iscalibrated to read mass in kilograms. You can see roughly how this works if you have a spring and a few masses. Hook each mass on the end of the spring, and hold the other end in your hand, and give the mass a slight tug, and watch it bounce up and down. The heavier masses will take longer to bounce up and down, because it has more inertia. (It will also stretch the spring more, because it has more weight on earth! What would you do with it in a 0-g environment?)
So, you ARE measuring "true mass" on earth, you are just using the gravity of the earth to help you. I think you wanted to know how you could measure true mass without using gravity at all.
I hope I have answered your question.

Answer 5:

A spring scale measures force F. If the mass of the object (measured by a comparative balance) is m. Then the Force measured by the spring balance (by Newtons Laws) is F = mg, where g is the acceleration due to gravity. F = 9.8 N for a 1 kg mass.
The spring scale is set up for an acceleration due to gravition of g = 9.8 ms^-2, so that when the spring scale says 1 g, it has actually calculated the force in N and divided by the g to obtain m. So the spring scale is calibrated for the surface of the earth (sea level) where g is 9.8 ms^-2.
If g were different, the spring scale would not work. This can be demonstrated by trying to use a spring scale in a moving elevator, or (better) by taking it to the moon. A mass of 1 g would be the same anywhere, but on the moon, it would have a weight (measured using a spring scale) that is approximately 1/6 g. So in a nutshell, weight is defined on the surface of the earth (sea-level) so that it is numerically equal to the mass.

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