![]() This means the upward normal force on the book by the table is about 0.5% less than the book's weight (at the equator). What about the vacuum chamber? The buoyant force of the air on the book is about 0.15% g. This means the net force on the book is not zero, and that in turn means the weight of the book is not quite cancelled by the table. It's a rather small acceleration, about 0.35% g at the equator, but it's not zero. The book rotates with the Earth, and except at the north or south pole, this rotation means the book is accelerating. The upward normal force exerted by the table and the downward gravitational force exerted by the Earth don't quite cancel. That's not quite true - unless the table in a vacuum chamber at the south pole. This tells us that the Earth curves spacetime and this creates the downwards force on you, however your mass also curves spacetime and this creates an upwards force on the Earth.įor a book lying on a table, for example, the weight is cancelled by the upwards reaction force from the table. To really understand what's going on you need to understand general relativity. With Newtonian gravity you just have to accept that there is a gravitational field in between you and the Earth, and this field transmits the force on you to the ground and the force on the ground to you. But now we seem to have the action and the reaction separated in space. So in (a) there is an equal and opposite pair of forces at the top of the box and another equal and opposite pair of forces at the base of the box. The confusion arises because we normally think of the action and reaction force as operating at the same point. The answer is that yes, there is indeed an equal and opposite force of $-mg$ on the Earth, so Newton's third law still applies. The question is whether there is an equal and opposite force upwards. There is still a downwards force $mg$ on you, and indeed that force is going to make you fall downwards. But how suppose we suddenly pull the box away as in (b). The box transmits your force to the ground, so the box applies a downwards force $mg$ on the ground and the ground applies an upwards force $-mg$ on the base of the box. You apply a downward force $mg$ on the top of the box, and by Newton's third law the box applies an upwards force $-mg$ on you. Suppose you're standing on a box as shown in (a) below: Similarly, the reason that masses (like, say, the interior of the Earth) don't get compressed any further is that any given volume of rock will be acted on by the downwards gravitational force and by the upwards pressure from the rocks below it. (And, of course, this gives an added reaction force downwards from the book on the table, which gets cancelled by a correspondingly larger reaction force from the floor on the table.) Conversely, if an object is not accelerating, then the net force on it is zero, and there must be additional forces that cancel out the gravitational one.įor a book lying on a table, for example, the weight is cancelled by the upwards reaction force from the table. If it is, then the total force will be nonzero and the object will accelerate (as per Newton's Second Law). Now, it's important to note that gravity is not usually the only force acting on any object at a given time. ![]() The reason you don't observe the Earth moving is that its acceleration is so small (on the order of 10 -25 m s -2) that it gets swamped in everything else, but it does happen. Thus, when you throw a ball of ~100g in the air, it experiences a gravitational force of 1N downwards, and in doing so it exerts a force of 1N upwards on the Earth. More specifically, every two pairs of masses feel a gravitational force that's proportional to the product of their masses and inversely proportional to the square of their relative distance, but more important is the fact that both masses feel the attraction to each other. ![]() Yes, every gravitational force in Newtonian mechanics has an equal and opposing force, and it usually acts on other mass. ![]()
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