Mechanical Advantage & Efficiency

advantage of machines machines help us do tasks; they give us an advantage example: a lever can be used to lift a load if the load is 36N and we only apply 12N of force to lift it, then we can figure out the advantage of the lever ie: (36N/12N = 3 X greater)

mechanical advantage there are 2 ways to look at this advantage: actual mechanical advantage (AMA) ratio of load force to effort force (FL/FE) ideal mechanical advantage (IMA) ratio of effort arm to load arm (dE/dL) most machines involve friction, so AMA<IMA

typical IMAs Machine IMA Ratio Equation wheel & axle ratio of radii rE/rL set of gears ratio of teeth count NE/NL set of pulleys count # of support strands see page 88 fig. 2 (count strands that pull up) inclined plane ratio of incline length and height length of incline/height

practice In an acrobatic demonstration, one person jumps onto the end of a plank (lever). This creates a large effort force of 920 N at the end of the board at a distance of 1.7 m from the fulcrum. A smaller person (460 N) located 3.1 m from the fulcrum, is launched into the air. Calculate: (a) the AMA of the board (b) the IMA of the board

NOTICE since AMA and IMA are calculated ratios they have no units!!! (units cancel out)

static and moving components when a machine is in static equilibrium, the law of the lever applies, so: dE/dL = FL/FE and the IMA equals the AMA when the components of the machine move, the effort force increases to account for friction, so: dE/dL > FL/FE and the IMA is greater than the AMA

force advantage (AMA) can be greater than 1, equal to 1, or less than 1 IF THEN AND FL/FE = 1 FL = FE dL = dE FL/FE > 1 FL > FE dL < dE FL/FE < 1 FL < FE dL > dE

efficiency the efficiency of a machine tells us how productive it is percent efficiency is the ratio of actual mechanical advantage to ideal mechanical advantage as a percentage % efficiency = AMA x 100 IMA

practice Calculate the percent efficiency in each of the following: (a) the distance ratio of a lever is 3.6 and the force ratio is 3.1 (b) the AMA of a wheel and axle is 6.0 and the IMA is 7.0