# How is weight $W = 0$?

One of my physics teachers told me that in the formula of calculating weight i.e. $$W = mg$$, $$m$$ is not equal to 0 until and unless you're travelling close to the speed of light. She added, that the acceleration due to gravity, $$g$$ is also never equal to 0 because for that either mass of Earth has to be 0 or the square of the radius infinite. My question is, if $$m$$ and $$g$$ are both non-zero, then how is weight equal to 0?

• And who said that "weight=0"? Aug 23 '20 at 4:31
• Please read this article Aug 23 '20 at 4:33
• Either you misunderstood your physics teacher, or that teacher is wrong. Objects gain mass as their velocity increases due to relativistic effects. In addition, the comment about the earth's radius being infinite indicates that your teacher is emphasizing a mathematical model more than physics, which shouldn't be done. In other words, mathematics is the language of physics, but mathematics is NOT physics. Aug 23 '20 at 16:19

## 2 Answers

See the problem with your argument is that Weight is not necessarily equal to mg. If you stand on a weighing machine then weight is equal to the Normal reaction with the machine.

If you stand on ground with no acceleration,then by Newton's Second Law$$N = mg$$ But if you stand in an accelerating lift,you are accelerating and hence: $$N - mg = ma$$ $$=>N= m(g+a)$$

Normal reaction will change depending on the magnitude and direction of acceleration.

In a nutshell ,Weight is the Normal reaction with the ground.

When you are in a free fall , there is no surface to provide Normal and hence Weight is zero and you will experience something called weightlessness.

Ever been on a roller coster?

Here you can actually feel your weight changing similar to that in a lift.

• Note that a some authors define weight as the force of gravity on an object. This especially happens in very elementary texts when the notion of weight is introduced as $mg$, but never "corrected". The word corrected is in quotes because the notion of weight is not definitively defined in physics; a minority of authors intentionally define it to mean the force of gravity on an object. To such authors, $W=mg$ near the surface of the Earth regardless of the state of motion. Aug 23 '20 at 14:17
• @garyp Sir I have never come across such a text. The texts I follow,some are which are internationally accepted, define Weight as Normal Force. In my understanding, this is the generally accepted notion of Weight. Anyways thank you for this information,I will keep it in mind. Aug 23 '20 at 14:57
• Your are right, the definition as normal force is generally accepted. But not universally. :-( Aug 23 '20 at 16:42
• I have a bunch of books on my shelf, some old, some new. Out of curiosity I started checking. The first was Newtonian Mechanics by A.P. French (1971 ed.). He defines weight as the force needed to keep an object in equilibrium against gravity. The second was the text by Halliday and Resnick (1966 ed.): "The weight of an object is the gravitational force exerted on it by the earth." I stopped checking, because I found examples of both in my first two tries. Aug 23 '20 at 17:26
• I prefer to make a distinction between weight (the force of gravity) and “effective weight” (the reading on a scale, which allows for various accelerations). Aug 23 '20 at 19:14

Weight is the force of gravity acting on a mass. If there is a mass in a gravitational field, it will have weight. What becomes zero is apparent weight, it is the reaction force by which you feel your weight. Without it, for example, under free fall you can't feel your own weight and this my friend is called "weightlessness". Reaction force is the force that a weighing machine measures.So if it's not applying any force(reaction) on you, then it will simply show you zero reading. But your weight is not zero, because your mass is not zero.