An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{2 ft.}{0.5 ft.} \) = 4

You might be wondering how having an effort distance of 4 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 4 times the resistance distance, the effort force must be \( \frac{1}{4} \) the resistance force. You're trading moving 4 times the distance for only having to use \( \frac{1}{4} \) the force.

A wheel and axle uses two different diameter wheels mounted to a connecting axle. Force is applied to the larger wheel and large movements of this wheel result in small movements in the smaller wheel. Because a larger movement distance is being translated to a smaller distance, force is increased with a mechanical advantage equal to the ratio of the diameters of the wheels. An example of a wheel and axle is the steering wheel of a car.

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

Mechanical advantage (MA) is the ratio by which effort force relates to resistance force. If both forces are known, calculating MA is simply a matter of dividing resistance force by effort force:

MA = \( \frac{F_r}{F_e} \) = \( \frac{5 ft.}{25.0 ft.} \) = 0.2

In this case, the mechanical advantage is less than one meaning that each unit of effort force results in just 0.2 units of resistance force. However, a third class lever like this isn't designed to multiply force like a first class lever. A third class lever is designed to multiply distance and speed at the resistance by sacrificing force at the resistance. Different lever styles have different purposes and multiply forces in different ways.