Last time we learned that the two T’s are all about, paying special attention to the Formula that’s formed by the belt angle of wrap around the pulley wheel.wrapping
Here again is the × e^{(μ}^{θ)} The tight side tension, T ; the friction that exists between the belt and pulley, denoted as _{2}μ ; and the length of belt coming in direct contact with the pulley, namely, θ. These last two terms are exponents of the term, e, known as Euler’s Number, a mathematical constant used in many circles, including science, engineering, and economics, to calculate a wide variety of things, from bell curves to compound interest rates. It’s a rather esoteric term, much like the term π that’s used to calculate values associated with circles.Euler’s Number was discovered in 1683 by Swiss mathematician Jacob Bernoulli, but oddly enough was named after Leonhard Euler. Its value, 2.718, was determined while Bernoulli manipulated high level mathematics to calculate compound interest rates. If you’d like to learn more about that, follow this link. The term Finally, the term θ measures the arc that’s formed by the belt riding along the surface of the pulley between points A and B, as shown by dotted lines. The is important to overall functionality of the assembly, because the proper amount of friction will allow the pulley-belt assembly to operate efficiently and without slippage.angle of wrap Next time we’ll present an example and use the
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