By George E. Drabble
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Extra resources for Applied Mechanics. Made Simple
The classic instance of this is planetary motion. The approximate circular motion of a planet around the Sun is produced by the gravitational pull of the Sun. If the latter were suddenly to be removed, the planet would fly outwards along a tangential path. Observe the difference between uniform motion in a circular path, and uniform motion in a straight line. We found in Chapter Two that the former constituted an acceleration, which is directed towards the centre of the circular path. Newton's Second Law re-states the first, but adds the vital word 'proportional'.
He would have to think more carefully, though, if his scale were a spring-balance type, and he were marketing apples on the Moon. The net result is that no matter what system of calculation is to be used, the units of force (in which is included weight) are to be clearly distinguished from those of mass, and are also numerically different from them. The weight of one pound of mass is 32-2 poundals of force; the weight of one gramme of mass is 981 dynes of force. For engineers, who find the pound force too familiar to reject, a new standard of mass has been devised: it is called the slug, and is a mass having a weight of approximately 32-2 pounds force.
Since the force concerned is that of gravity, body B must be the Earth. Are we to assume, then, that Newton's Third Law makes the absurd assertion that the Earth is being pulled upwards by your body? It is indeed, and by the same force as your weight. Unfortunately, the Earth is so big that we tend to lose sight of it as an independent body capable of being acted upon by, and responding to, forces. The situation becomes clearer if we make a simple model of a gravitational system between two bodies.