In our last blog we saw how adding extra pulleys resulted in mechanical advantage being doubled, which translates to a 50% decreased lifting effort over a previous scenario. Pulleys are engineering marvels that make our lives easier. Theoretically, the more pulleys you add to a compound pulley arrangement, the greater the mechanical advantage — up to a point. Eventually you’d encounter undesirable tradeoffs. We’ll examine those tradeoffs, but before we do we’ll need to revisit the engineering principle of work and see how it applies to compound pulleys as a work input-output device.
Pulleys as a Work Input-Outut Device
The compound pulley arrangement shown includes distance notations, d1 and d2. Their inclusion allows us to see it as a work input-output device. Work is input by Mr. Toga, we’ll call that WI, when he pulls his end of the rope using his bicep force, F. In response to his efforts, work is output by the compound pulley when the urn’s weight, W, is lifted off the ground against the pull of gravity. We’ll call that work output WO.
In a previous blog we defined work as a factor of force multiplied by distance. Using that notation, when Mr. Toga exerts a force F to pull the rope a distance d2 , his work input is expressed as,
WI = F × d2
When the compound pulley lifts the urn a distance d1 above the ground against gravity, its work output is expressed as,
WO = W × d1
Next time we’ll compare our pulley’s work input to output to develop a relationship between d1 and d2. This relationship will illustrate the first undesirable tradeoff of adding too many pulleys.
Copyright 2016 – Philip J. O’Keefe, PE