Units about weight

Question

We know that weight is measured in Newtons. Since, $weight= mass\times gravitational~acceleration$. What will be the units of Newton? Will that be $N = kg\times g$ ? But we always measure our weight using the unit $kg$! Are we right in doing so?

Answer 1

Since $F=ma$ and the unit of force is the Newton, which is the multiplication of the units of mass and acceleration. That is $kg\times ms^{-2}$. So the Newton is equivalent to $kg ms^{-2}$. It also has other equivalences when we look at electromagnetism and other areas of physics, but this is usually the first form you are introduced to.

Answer 2

Bathroom scales - the type you are talking about when referring to your own weight - do actually measure weight. So the truth is a little more complex than other answers have pointed out.

What we should say when a bathroom scales gives your "weight", as say 70 kg, is that your weight is actually $70 g$ Newtons, where $g$ is the value of gravitational acceleration that is assumed in the calibration of the scales. Sometimes there is an adjustment to change this assumed value which could be calibrated if you had an accurate test mass that you could put on the scales.

If not, and you want to accurately estimate your mass, then you need to know what value of $g$ was assumed, and the local value of gravity $g_0$, since your mass is actually $70 g/g_0$ kg.

The local gravity across the Earth's surface varies by as much as 0.5% and so the scales, unless re-calibrated would report your "weight" as varying by 0.5% in sympathy with this variation. Similarly the "weight" reported by the scales if you went up and down in a lift would vary.

Note that this discussion refers to spring or stress-gauge balances. If you measure "weight" using something like an old-fashioned pair of scales or a beam balance, then you are directly comparing your mass against a test mass in the same gravitational field. Therefore this method of "weight" measurement tells you accurately what your mass is directly (in kg) and to estimate your weight you would then have to multiply by the local value of gravity.

Answer 3

But we always measure our weight using the unit kg! Are we right in doing so?

No. You are correct in thinking that we are wrong in doing so.

Actually, what is wrong with it, is our use of the word weight. If you instead of saying "My weight is 70 kg" said "My mass is 70 kg", then everything is fine.

When you stand on a scale, the scale measures the force you exert, which is your weight $W$ in $\mathrm{[N]}$, and then by itself multiplies with $g$ to end up showing you your mass $m$ on the screen. It simply uses the equation:

$$W=mg$$

to find $m$. The calibration of the scale is the reason that the $g$ fits. If you brought a scale made on Earth to the Moon, it would be wrong! Since gravity is about 6 times weaker, which means that $g$ at the moon is 6 times smaller and you now weigh 6 times less, then (since the scale still uses the Earth's $g$) the mass (which should be constant nomatter where you are) that the scale shows on the screen will be 6 times too small as well:

$$W_{moon}=mg_{Earth} \implies \frac{1}{6}W_{Earth}=mg_{Earth} \implies \frac{1}{6}\frac{W_{Earth}}{g_{Earth}}=m$$

What will be the units of Newton? Will that be $N=kg \times g$?

No, you forgot to put the units of the "gravity" $g$ you mention in instead of $g$. Since $g$ that you call "gravity" is a gravitaional acceleration with units of $[m/s^2]$, the right unit equivalence is:

$$[N]=[kg] \cdot [m/s^2]$$

Answer 4

All right, read closely.

So what is weight? Weight is nothing but the Force that your body exerts in it's surrounding. If a body's mass is around 5 then the force exerted by your body on the ground is going to be 50N.

So how I got to that answer?

You seem to be a 10th Grader from your age. Maybe 9th Grader, but I think you must have learned in your School, the formula for finding Force.

$F = m \times a$

From this we can obtain,

$F = 5 \times 10 $

$F = 50 N$

But you must have know that already, I guess. Now, the units are going to be $kgm/s^2$ itself, but since it's really tedious to write it this big, we thought why not shorten the name and then call it Newton. I mean newton is a big name in classical Mechanics so giving him respect is not like a big deal by naming a unit Newton.

So they both are same, the later is only a bit more convenient way. Again in India most teachers confuses the student because they themselves are confused. The unit of mass is KG. The weight you have is also in K.G.

When you stand on the Weighing Machine, you actually are measuring your mass because the machine has already considered the Force due to gravity acting on your body has to be stopped, to show a precise and accurate answer. It just went out to be really wrong in Society. It once spread as weight and won't even diminish.

It's all just a misunderstanding on the parts of many Indian books and teachers. I don't know about the rest of the world.

Answer 5

Yes we are not doing right. Instead we should use 'kg' to measure our weight. If we use a scale made for earth and measure our weight in a planet with a different 'g',we will not get the right measurement.