Chapter 1414.3 Mechanical Advantage and Efficiency

Mechanical Advantage The mechanical advantage of a machine is

the number of times that the machine increases an input force.

Actual Mechanical Advantage Actual mechanical advantage = output force

÷ input force

Ideal Mechanical Advantage Actual mechanical advantage can be

increased by reducing friction.The ideal mechanical advantage is the

mechanical advantage in the absence of friction.

Because friction is always present, the actual mechanical advantage of a machine is always less than the ideal mechanical advantage.

Ideal Mechanical AdvantageIdeal mechanical advantage = input distance

÷ output distance

Efficiency Efficiency = (work output ÷ work input ) x

100%

Because there is always some friction, the efficiency of any machine is always less than 100 percent.

Simple MachinesThere are 6 types of simple machines:LeverWheel and axleInclined planeWedgeScrewPulley

LeversA lever is a rigid (non-bending) bar that is

free to move around a fixed point called a fulcrum.

Levers To calculate the ideal mechanical advantage

of any lever, divide the input arm by the output arm.

The input arm is the distance between the input force and the fulcrum.

The output arm is the distance between the output force and the fulcrum.

See figure 13 on page 428.

LeversFirst-class levers have the fulcrum between

the input and output force.Second-class levers have the output force

between the input force and fulcrum.Third-class levers have the input force

between the output force and fulcrum.

Wheel and AxleA wheel and axle is a simple machine that

consists of 2 disks or cylinders, each one with a different radius.

See figure 14 on page 430.

Wheel and AxleTo calculate the ideal mechanical advantage

of the wheel and axle, divide the radius (or diameter) where the input force is exerted by the radius (or diameter) where the output force is exerted.

Inclined PlanesAn inclined plane is a slanted surface along

which a force moves an object to a different elevation.

See figure 15 on page 430.

Inclined PlanesThe ideal mechanical advantage of an

inclined plane is the distance along the inclined plane divided by its change in height.

Wedges A wedge is a V-shaped object whose sides are

2 inclined planes sloped toward each other.See figure 16 on page 431.A thin wedge of a given length has a greater

ideal mechanical advantage than a thick wedge of the same length.

Screws A screw is an inclined plane wrapped around

a cylinder.See figure 17 on page 431.Screws with threads that are closer together

have a greater ideal mechanical advantage.

Pulleys A pulley consists of a rope that fits into a

groove in a wheel.See page 432 figure 19.The ideal mechanical advantage of a pulley or

pulley system is equal to the number of rope sections supporting the load being lifted.

Compound MachinesA compound machine is a combination of 2 or

more simple machines that operate together.Examples: car, clock, washing machine