The Newton: SI unit of force
The Newton is the SI unit of force. Strictly defined: the force that will give a mass of 1 kilogram an acceleration of 1 meter per second per second. It is not in everyday use. When did you last read a recipe that required you to add one newton of flour to a cake mixture? There is no logical reason for not doing so. A force of 1 Newton on the balance pan is approximately the force exerted downwards by 100 grams of flour on the pan.
So why not use kilograms per square metre also for the stress strain diagram? The pompous answer is that using Newtons allows this diagram to be used on a distant planet with a different mass. Weight is the expression of the force exerted by the earth on the mass of an object. The mass is the fundamental quantity, the weight, even on earth, varies with the position of the object. On the moon, 100 grams of flour would make a very big cake, if you measured it with a spring balance. 1 Newton of flour would work just like on earth.
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