Last time we introduced the engineering expert. Today we’ll examine . We’ll begin with a the math behind the compound pulley representation and follow up with an active one in our next blog.static The F, _{1}F, and _{2}F. Together, these three forces work to offset the weight, _{3}W, of a suspended urn weighing 40 lbs. Weight itself is a downward pulling force due to the effects of gravity. To determine how our F, we must first calculate the tension forces _{3}F and _{1}F. To do so, we’ll use a _{2}free body diagram, shown in the green box, to display the forces’ relationship to one another.
The free body diagram only takes into consideration the forces inside the green box, namely F, and _{2}W. For the urn to remain suspended stationary in space, we know that F are each equal to one half the urn’s weight, because they’re spaced equidistant from the _{2} axle, which directly supports the weight of the urn. Mathematically this looks like,pulley’s
Because we know F, we also know the value of _{2}F, thanks to an engineering rule concerning _{3}. That is, when a single rope is used to support an object with pulleys, the tension force in each section of rope must be equal along the entire length of the rope, which means pulleysF. This rule holds true whether the rope is threaded through one simple pulley or a complex array of fixed and moveable simple pulleys within a _{1} = F_{2 }= F_{3}. If it wasn’t true, then unequal tension along the rope sections would result in some sections being taut and others limp, which would result in a situation which would not make lifting the urn any easier and thereby defeat the purpose of using compound pulley.pulleys If the urn’s weight,
÷ 2 = 20 poundsMr. Toga needs to exert a mere 20 pounds of personal effort to keep the immobile urn suspended above the ground. It’s the same effort he exerted when using the improved simple pulley in a previous blog, but this time he can do it from the comfort and safety of standing on the ground. Next time we’ll examine the math and mechanics behind an active _{1} , F_{2} , and F_{3.}
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