Newtonian Mechanics – What is Weight?

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When a book is kept on the table than gravity of earth is attracting the book downwards and gravity of book attract earth this is action reaction pair

Now here are two more force acting normal reaction force which is pushing the book upwards and an action force pushing the table downwards

So what basically weight is the force that is pushing the table or the force by which earth attract the book (force by which book attract the earth) although all of them will have same magnitude but still?

Best Answer

There seem to be at least two schools of thought.

In terms of attraction in a gravitational field
One definition of the weight of a body is the gravitational attraction on a body and so weight equal to $mg$ where $m$ is the mass of the body and $g$ is the gravitational field strength.
With this definition weight varies only in so far as the gravitational field strength, on Earth $g = 9.8 \,\rm m/s^2$ approximately, varies.
When you and the scales are accelerating, the scales are reading your apparent weight.
When you are orbiting the Earth you appear to be weightless although you must still have a weight otherwise there would not be a force present causing the centripetal acceleration to keep you in orbit.

In terms of the reading on a spring balance
After watching 8.01x - Lecture 7 - Weight, Weightlessness in Free Fall, Weight in Orbit you are left in no doubt as to Professor Lewin's definition; the weight of an object is the force exerted by an object on some “scales” whether it be a push or a pull.
The object “feels” its weight because of the Newton's third law reaction on it, the force exerted by the scales on the object.
So when you are in a lift and the cable breaks you are weightless (the scales register a zero reading) and you feel weightless (the lift floor is not pushing up on you).
If by some means the lift accelerated downwards with an acceleration greater than $g$, the scales, now on the ceiling of the lift, would register a reading and so you have a weight.
The quantity $mg$ Professor Lewin never calls weight; he calls it gravity or gravitational attraction or something similar.