[2015] Engineering Fundamentals 03: Mass and Force in English Unit Systems [with closed caption]
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In the previous video I gave an overview of the SI unit system. In this video I would like to briefly discuss the U.S. Customerary unit system and the American Engineering system. Listed in this table are some common units in US customary unit system and American engineering system. As you can see they are both based on foot-pound and second and many of the units are the same. The major difference lies in the units for mass and force. In American engineering system, the units for mass and force are both pound. To distinguish we must use the subscripts m for mass and f for force. In US customary unit system, on the other hand, pound is only used as the unit for force, and the unit for mass is slug. Therefore it is less confusing in the US customary unit system. I will explain these units later. Hopefully by the end of this video you would gain some clearer understanding on these units. In order to clearly understand these units it is important that we understand that mass and weight are two completely different concepts. Mass is the amount of substance an object possesses, versus weight is actually a force. To be specific, weight is the gravitational force exerted by the earth to an object on the earth. Since weight is a force, its relation to mass is also governed by Newton’s second law, that the force equals to mass times acceleration. If you recall in the SI unit system, The unit of force is derived based on Newton’s second law, that one newton equals to 1 kg times 1 meter per second squared. Here kilogram is the unit of mass and meter per second squared is the unit for acceleration in SI unit system. Now for U.S. customary unit system, we want to write an equation in the same format. Here pound is the unit for force in US customary unit system and foot per second squared is the unit for acceleration. So we want this blank area to be the unit for mass in US customary unit system. And that unit is slug. Therefore defined according to Newton’s second law, one slug equals to 1 pound force divided by 1 foot per second squared. So how do we determine the weight of an object? For that we need to know the gravitational acceleration constant, which technically is a variable but normally takes the value of 9.81 in meter per second squared, in SI unit system. And you probably know this already. Therefore in SI unit system for an object with a mass of 1 kg its weight is calculated by this equation. Its mass is 1 kg, g the gravitational acceleration is 9.81 meter per second squared, therefore the weight force is 9.81 newton. In U.S. customary system, for an object with a mass of one slug, its weight is also determined using this equation. But the gravitational acceleration g needs to be converted into the U.S. customary unit system, as well, which is approximately 32.2 foot per second squared. Therefore the weight of an object with a mass of 1 slug is calculated this way to be 32.2 pound. However according to the American Engineering System AES, if an object has a weight of 1 pound force then it must have a mass of 1 pound mass. Therefore in the previous example, for an object with a mass of 1 slug we calculated that is weight is 32.2 pound which is the same as 32.2 pound force, that means that the mass of this object must be 32.2 pound mass. And that is the relation between the two units slug and pound mass.

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