# What is mass divided by weight?

###### April 09, 2014 12:00AM

It's (1) divided by (the acceleration of gravity in the place where that mass has

that weight):

weight = mass x g (where g is the acceleration due to gravity)

⇒ mass/weight = mass/(mass x g)

= 1/g

On the earth, g ≈ 9.81 ms-2 ⇒ mass/weight ≈ 1/9.81 ms-2 ≈ 0.102 m-1s2

On the moon, g is approx 1/6 that of the earth, ⇒ mass/weight ≈ 6/9.81 ms-2 ≈ 0.612 m-1s2

If the questioner really meant weight divided by mass it gives the acceleration

due to gravity in that place otherwise I'm not sure of a use of knowing the

reciprocal of the acceleration due to gravity that the questioner asked.

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If you ask a scientist, that's true answer in the sense that a mass M experiences

a gravitational force Mg and if you measure weight in units of force (which

nobody does). But anyone else would be surprised to learn that a mass M (say

10 grams) would have a weight of anything else but M grams (10 grams).

Sometimes expressed as "grams weight" often just grams for short. If you pick

up a Kilogram, even a scientist would say "its weight is 1 kilogram". The

gravitational force on it is 1g, so if you let it go it will accelerate at a rate force

over mass, which is g. So the answer depends on your units of mass and weight.

That's why science lessons tend to avoid use of "weight". In outer free space

mass would be measured by (say) tension in the string if you whirl it on the end

of it around your head, but the weight (measured by a spring balance) would be

zero (precisely as described in the first answer above, with g=0).

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The problem with discussing mass and weight in the same units, and the reason that this masked contributor is waging a one-man battle to make the distinction recognized and acknowledged by users of this website, is the new problem that

you have now that the space age is here.

As long as we were all irrevocably bound to the Earth, one kilogram of mass would always weigh one kilogram, if you like it that way. We could afford to be sloppy about it, with hardly one out of ten men-on-the-street knowing or caring about the difference, and nobody ever had a problem with it.

But now that some of us have already slipped these surly bonds ... and among

the general population, the younger you are, the better the chance that you will

do so one day before you're done ... those who ignored the distinction begtween

mass and weight all through school, or never even encountered it there, are

poised to step into an inconvenient pile. Because as soon as you pack for your

trip to anywhere else away from Earth, and take along your lucky kilogram,

you're due for a shock when you step out at your destination: Your kilogram

doesn't "weigh" a kilogram there. It weighs something else. If you're on the

moon, for example, your kilogram weighs 0.165 kilogram ! That's the

shock I'm trying to avoid, because if you think the straight dope is too complex

for people to handle now, you haven't seen anything yet.