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An object is falling and it weighs 25 kg (on a scale, presumably). What is its mass?

I know that weight is measured in Newtons and mass in kilograms, but what if a problem states that something weighs in kilograms? Would I still use $\text w=mg$?

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Could you please add your actual problem in your question so that we could say something useful..? –  Waffle's Crazy Peanut Nov 13 '12 at 16:04
    
An object is falling and it weighs 25 kgs. What is its mass? That's the question. It's a tricky one - do I use w=mg, or do I just say 25kg? –  rookky12 Nov 13 '12 at 16:05
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Sounds like a trick question. 25kg is a measure of mass, so that's the answer. In everyday usage the word weight often means mass, so the wording of the question isn't completely wrong, although in Physics weight normally refers to the measure of gravitational force on an object, which can vary depending on where it is located. –  Jason Davies Nov 13 '12 at 16:51
    
Yeah, it's a tricky question. I'll go with 25 kg. Thanks :). –  rookky12 Nov 13 '12 at 17:13

3 Answers 3

up vote 2 down vote accepted

I've seen some books use kg for kgf (kilogram-force), even though they shouldn't have conflated them.

But in this case it's not too harmful: if 25 kg means mass, as it should, then it the answer is direct. On the other hand, if 25 kg really means 25 kilogram-force, then the answer is the same under the assumption of standard gravity, because $1\,\text{kgf}$ is by definition $(1\,\text{kg})(9.80665\,\text{m/s}^2)$, the weight of 1 kg under 1 standard gravity.

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Thanks. I'll assume that the mass is 25kg. –  rookky12 Nov 13 '12 at 17:56

OK, I should mention something (related to the g-force)...

As an object is under the free-fall due to gravity, acceleration $a$ equals the acceleration due to gravity $g$ and thereby, the mass of the object measured would be the same. These are the consequences of inertial mass & gravitational mass. Whenever you try to measure the mass of the free-falling object, you should have to move accordingly with the rest frame of the object. The resulting effect is - You would measure the mass again & again. This shows the fact that, The weight is zero during a free-fall.


Hence, there's a misconception with your question. The mass would be definitely the same.

This Wiki article on Weightlessness would be useful...

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The weight of an object is a measurement of how hard a force(in our case gravity) is pulling on an object. so W = mg, where W - is the weight. in our case W is G (Gravitational force) So G = mg => m = G/g => m = 25/9.8 => m = 2.5 kg. If you're problem states that weight is measured in kg, then it is definitely wrong. Weight is measured in Newtons and mass in kg

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Instead of using reserved letters (fundamental constants) like $G,c,h$, one could make use of common terms like $F$ itself for Force. You could differentiate those by using subscripts ($F_g$ like that...) –  Waffle's Crazy Peanut Nov 13 '12 at 19:02
    
I agree that using you're form might be a better approach to understand the concept. But in terms of physics, when you solve a problem for an exam, you should use those fundamental constants. It's like a universal language –  apahidean.iancu Nov 13 '12 at 19:55
    
Nothing so important, I just pointed out that you're assuming $G$ as gravitational force. It's not a big deal. But, some users would be confused "the moment they see it..!" That's all :-) –  Waffle's Crazy Peanut Nov 13 '12 at 20:05

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