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:

1.actual mechanical advantage (AMA) ratio of load force to effort force (FL/FE)

2.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