Mechanical advantage is the ratio of output force to input force.

Machines multiply forces.

One person could lift an elephant—quite a heavy load—with a properly designed system of ropes and pulleys!

MA = Fo

Fi

Output force (N)

Input force (N)

mechanicaladvantage

A lever includes a stiff structure (the lever) that rotates around a fixed point called the fulcrum.

Levers are useful because you can arrange the fulcrum and the input arm and output arm to adjust the mechanical advantage of the lever.

Each class of levers is defined by the location of the input and output forces relative to the fulcrum.

Many machines require that rotating motion be transmitted from one place to another.

Gears change force and speed.

The gear ratio is the ratio of output turns to input turns.

You can predict how force and speed are affected when gears turn by knowing the number of teeth for each gear.

To = Ni

Ti No

Number of teethon input gearTurns of output gear

Turns of input gearNumber of teethon output gear

Ropes and strings carry tension forces along their length.

If the rope is not moving, its tension is equal to the force pulling on each end.

A ramp is a simple machine that allows you to raise a heavy object with less force than you would need to lift it straight up.

The mechanical advantage of a ramp is the ramp length divided by the height of the ramp.

A screw is a rotating ramp.

You find the mechanical advantage of a screw by dividing its circumference by the lead.

A wedge is like a ramp that can work while in motion (a ramp is always stationary).

A wedge has a side that slopes down to a thin edge.

The mechanical advantage for a wedge is inversely related to the size of the wedge angle.

A wheel rotates around a rod called an axle.

The mechanical advantage is the ratio of the radius of the wheel to the radius of the axle.

The wheel and axle move together to move or lift loads.

A crowbar is a type of lever that you use to pull a nail out of a piece of wood.

If the handle of a crowbar is 40 centimeters and the foot is 2 centimeters, what is its mechanical advantage?

1. Looking for: › …mechanical advantage of lever

2. Given› …input arm = 40 cm; output arm = 2 cm

3. Relationships:› M.A. = Length of input arm

Length of output arm4. Solution

› M.A. = 40 cm ÷ 2 cm = 20

Complete “Your Turn” problems on p. 215

Complete Skill Sheet