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### Mass vs. Weight

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Date: 05/27/99 at 14:56:08
From: ryan
Subject: Physics (F = mg)

If you calibrated a scale to read lb. (mass) at g = 32.192 ft/s^2, and
you took this scale to the moon where g = 5.32 ft/s^2, placed a moon
rock onto the scale and the scale read 13.37, what would be the mass
of the rock on the moon?  What would be the weight of the rock on the
moon?

My question concerns the calibration of the scale at one g, then going
to the moon and taking masses at another g. Is this a proportionality
problem?
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Date: 05/28/99 at 08:47:32
From: Doctor Rick
Subject: Re: Physics (F = mg)

Hi, Ryan, thanks for your question!

There is a very important piece of information that you have left out.
What kind of scale is this? It makes a huge difference whether it is a
balance or a spring scale. I assume it is a spring scale, but before I
get to that, let me copy an answer I sent to a teacher who asked:

>weight, and now have a follow question:
>
>We have a triple beam balance that claims to measure mass. It
>measures in gram units, so we are led to believe it is measuring
>mass. However, it appears to be like any other scale that truly
>measures the force that the earth's gravity is putting on an object.
>(Newtons) I realize mass and weight are used interchangeably, and
>hope you can provide me with a concise explanation that I can share
>with my students.

Hi, Chris. Good question! As a matter of fact, triple beam balances do
measure mass, not gravitational force. The same is true for the simple
two-pan balances that come with the set of "weights." On the other
hand, spring scales like those we have in our bathrooms measure
gravitational force.

You see, a balance works by comparing the force of gravity on the
sample you are weighing with the force of gravity on standard masses.
In the case of the two-pan balance, you just use the set of weights to
make up a mass equal to that of your sample. In the case of the
triple-beam balance, you have fixed weights but you adjust the lever
arms to get balancing torques.

If you were to take the balance to the moon where the gravitational
force is less, the force pulling on your sample will be less; but the
force pulling on the standard masses will be reduced in the same
proportion. The result is that you will need exactly the same masses
(or the same lever arms) to balance your sample.

A spring scale, on the other hand, works by comparing the force caused
by gravity with the force exerted by a spring that is compressed a
certain amount. The heavier the weight (and this time it really is
weight), the more the spring has to be compressed to get a matching
spring force.

If you stood on a spring scale on the moon, your body would exert less
force on the scale. The spring still has the same spring constant that
it had on the earth, so it would not have to compress as far to give
the lower force; and the scale would say you weigh less.

In conclusion, your triple beam balance uses gravity as sort of an
intermediary in its measurement, but it compares mass against mass. It
wouldn't work in space where there is no gravitational force (in the
reference frame of the free-falling balance). But in any place where
there is a uniform gravitational field, it should give the same
measurement of mass. Spring balances, though, compare force against
force, so they measure weight, not mass.

------

Now back to you, Ryan. That may help you understand the background of
this problem. Did you catch the part about spring scales measuring
force? When the scale reads m pounds, it is actually detecting a force
of mg pound-feet per second squared, where g is the acceleration of
gravity on EARTH since that's where it was calibrated.

Knowing a reading m (whether on earth or on the moon), you can
calculate the force detected by the scale. In the problem, this force
is the gravitational force exerted by the moon on the mass. From this
and the acceleration of gravity on the moon, you can calculate the
actual mass.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Physics/Chemistry

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