![]() Expressing F in newtons we now get a-for any acceleration, not just for free fall-as "īy Newton's second law, the acceleration a of an object is proportional to the force F acting on it and inversely proportional to its mass m. ![]() "When you measure what you are speaking about and express it in numbers, you know something about it, but when you cannot express it in numbers your knowledge is of a meager and unsatisfactory kind. Lord Kelvin, leading British scientist in Queen Victoria's era, was quoted as once saying We now can express in numbers the dependence of acceleration on force and mass. Earlier this was called "a force of one kilogram of weight, " a convenient unit for rough applications (1 kg = 9.8 newton), but not for accurate ones, because of the variation of g around the globe. Equation (1) not only shows that weight is proportional to mass, but-assuming it is measured in kilograms-it introduces a unit of F, named (no surprise!) the " newton."īy that equation, a force of one newton acting on one kilogram of mass accelerates it by 1 m/sec 2, so the force of gravity on one kilogram of mass is about 9.8 newtons. In the MKS system the effective value of g varies from 9.78 m/s 2 on the equator to 9.83 m/s 2 at the poles, due to the Earth's rotation (see section #24a). if by mistake you mix MKS units with grams or centimeters (or pounds and inches), and you may end up with some mighty strange results! That convention is known as the MKS system: as long as one's formulas contain only quantities derived by that system, they will be consistent and correct. Let us therefore choose from now on to measure distance in meters, mass in kilograms and time in seconds. Yes, proportionality allows one to add on the right some constant multiplier, but we won't, because now we want to define some units of F.Īll quantitative formulas and units in physics depend on the units in which three basic quantities are measured- distance, mass. Where g is the acceleration of gravity, directed downwards. The force of gravity is proportional to mass m, so we can write In today's terms we say that both weight and inertia are proportional to the mass of the object, the amount of matter which is contains.Ĭonsider free fall due to gravity. Newton proposed that the reason was that although the force of gravity on the heavier object (its weight) was twice as large, so was its inertia.
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