Last time we saw how compound increasedto the lifter, mechanical advantage being an engineering phenomenon that makes lifting weights easier. Today we’ll see how the mechanical advantagemechanical advantage increases when fixed and movable moreare added to the compound pulley arrangement we’ve been working with.pulleys
The image shows a than the one we previously worked with. To determine the pulley of this pulley, we need to determine the force, mechanical advantageF, Mr. Toga exerts to hold up the urn._{5} The urn is directly supported by four equally spaced rope sections with tension forces F, _{2}F, and _{3}F. The weight of the urn, _{4}W, is distributed equally along the rope, and each section bears one quarter of the load. Mathematically this is represented by,
4If the urn’s weight wasn’t distributed equally, the bar directly above it would tilt. This tilting would continue until equilibrium was eventually established, at which point all rope sections would equally support the urn’s weight. Because the urn’s weight is equally distributed along a single rope that’s threaded through the entire all rope sections, including the one Mr. Toga is holding onto. Therefore,
4 Stated another way, the force,
4 If the urn weighs 40 pounds, Mr. Toga need only exert 10 pounds of bicep force to keep it suspended, and today’s compound mechanical advantage, MA, of,
It’s clear that adding the two extra we’d continue to increase his pulleys, and he’d be able to lift far heavier loads with a minimal of effort. Is there any end to this mechanical advantage, No, but there are undesirable tradeoffs. We’ll see that next time.mechanical advantage?Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |