The Wedge and Screw Study Guide for McGraw-Hill's Firefighter Exams
A wedge is an inclined plane that tapers to a sharp edge. It is used to increase force. Double wedges are made up of two inclined planes and are used to split (e.g., fireplace logs), fasten, or cut. However, a wedge can also be one sloping surface (single wedge) such as that used by firefighters as a chock or doorstop. When used for cutting, the longer and thinner the wedge, the less effort (force) is required to overcome resistance. You can enhance the mechanical advantage of an axe, a type of double wedge, by sharpening it. Effort (force) is applied to the thicker edge of the wedge and is transferred to the thinner end. The wedge is also used to change the direction of force. When force is applied downward on a double wedge, it will push out in two directions helping to push things apart at right angles. Unlike the inclined plane, the wedge moves. For example, when a wedge is used to split a log, it is the log that remains in place while the wedge moves through it.
Many common objects are double wedges. Nails, for example, are wedges used to fasten objects together. The tip of a slotted screwdriver is a simple wedge. Knives, axe heads, chisels, and scissors are sharpened double wedges used for cutting.
To ascertain the mechanical advantage of a single wedge when it is used as a chock, simply use the same formula as that for the inclined plane, as shown below:
To ascertain the mechanical advantage for a double wedge use the formula:
Example: What is the mechanical advantage of a single wedge with a length of slope of 18 cm and height (thickness) of 6 cm being used to chock open a door by firefighters stretching hose line?
Example: Which double wedge, A or B, being used to split logs, has the greater mechanical advantage?
MA for double wedge A = 15 cm/5 cm = 3
MA for double wedge B = 15 cm/3 cm = 5
Double wedge B has the greater mechanical advantage.
A screw is a simple machine similar to an inclined plane or a wedge, but in a screw the incline wraps around a shaft. A screw converts rotational motion to linear motion. The pitch of a screw is the distance between its threads; this is the distance the screw will advance during one complete rotation.
To find the mechanical advantage that a screw provides, you have to know the pitch. The mechanical advantage of a screw is calculated by dividing the circumference of the screwdriver handle by the pitch of the screw.
The circumference of the screwdriver handle can be considered the effort distance and the pitch of the screw can be considered the resistance force.
Example: A screw with 10 threads per inch is being turned by a screwdriver that has a handle with a radius (r) of 1 inch. What is the mechanical advantage? To determine the mechanical advantage (MA), first calculate the circumference of the handle of the screwdriver.
C (circumference) = 2πr
C = 2 (3.14)(1 inch)
C = 6.28 inches
When using a screwdriver, the mechanical advantage of a screw is calculated as follows: