# The origin of the wedge is unknown, because it has been in use as early as the stone age.

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2 Lever A lever is a rigid object that is used with an appropriate fulcrum or pivot point to change the mechanical force that can be applied to another object. The principle of leverage can be derived using Newton's laws of motion, and modern statics. The lever only allows one to trade effort for distance or vice versa. The earliest remaining writings regarding levers date from the 3rd century BCE and were provided by Archimedes. Give me the place to stand, and I shall move the earth is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria). In ancient Egypt, builders used the lever to move and uplift obelisks weighing more than 100 tons. There are three classes of levers representing variations in the location of the fulcrum and the input and output forces. First-class levers A first-class lever is a lever in which the fulcrum is located in between the input force and the output force. In operation, a force is applied (by pulling or pushing) to a section of the bar, which causes the lever to swing about the fulcrum, overcoming the resistance force on the opposite side.the fulcrum is the center of the lever on which the bar (as in a seesaw) lays upon. This supports the effort arm and the load. o seesaw (also known as a teeter-totter), crowbar, claw hammer (removing nails), pliers (double lever), scissors (double lever), wheel and axle, load arm, and effort arm principle, oars, when used for rowing, steering, or sculling, can opener, bottle opener, bicycle hand brakes Second-class levers In a second-class lever the input is located to the far side of the bar, the output is located in the middle of the bar, and the fulcrum is located on the side of the bar opposite to the input. o wheelbarrow, nutcracker, door, crowbar, stapler, diving board, wrench

3 Third-class levers It is to be noted that for this class of levers, the input effort is higher than the output load, which is different from the first-class and second-class levers. However, also notice that the input effort moves through a shorter distance than the output load. Thus it still has its uses in making certain tasks easier to do. o human arm, tweezers, slings, fishing rods, tools such as a hoe or scythe, baseball bat, shovel, broom, staple remover, golf club, hockey stick, human mandible Wheel and Axle The wheel and axle is a simple machine. It consists of a large wheel that turns an axle around which a cord is wound. A heavy weight attached to the cord can be lifted more easily because of mechanical advantage. The wheel and axle can be considered to be a lever in which the radius of the wheel is the effort arm and the radius of the axle represents the resistance arm. It also is a single forced machine. By changing the short distance of lifting, the force is less because the work always stays the same. Screwdrivers, doorknobs, windmills, gears, and Chain Falls are all examples of the wheel and axle.

4 Pulley A pulley is a wheel with a groove along its edge, also called a sheave, for holding a rope or cable. Pulleys are usually used in sets designed to reduce the amount of force needed to lift a load. However, the same amount of work is necessary for the load to reach the same height as it would without the pulleys. The magnitude of the force is reduced, but it must act through a longer distance. The effort needed to pull a load up is roughly the weight of the load divided by the number of wheels. The more wheels there are, the less efficient a system is, because of more friction between the rope and the wheels. Pulleys are one of the six simple machines. It is not recorded when or by whom the pulley was first developed, but most likely came from Eurasia. The basic building block of a pulley, the wheel, was unknown to cultures in the western hemisphere, sub-saharan Africa and Australia until relatively recent encounters with Eurasians. It is believed however that Archimedes developed the first documented block and tackle pulley system, as recorded by Plutarch. The types of pulleys are Fixed (Class 1) A fixed or class 1 pulley has a fixed axle. That is, the axle is "fixed" or anchored in place. A fixed pulley is used to redirect the force in a rope (called a belt when it goes in a full circle). A fixed pulley has a mechanical advantage of 1. Movable (Class 2) A movable or class 2 pulley has a free axle. That is, the axle is "free" to move in space. A movable pulley is used to transform forces. A movable pulley has a mechanical advantage of 2. That is, if one end of the rope is anchored, pulling on the other end of the rope will apply a doubled force to the object attached to the pulley. Compound A compound pulley is a combination fixed and movable pulley system. o Block and tackle - A block and tackle is a compound pulley where several pulleys are mounted on each axle, further increasing the mechanical advantage. Plutarch reported that Archimedes moved an entire warship, laden with men, using compound pulleys and his own strength.

5 Mathematics The ideal mechanical advantage (IMA) of a simple machine depends strictly on the geometry of the machine. This is the theoretical maximum mechanical advantage produced by a machine and is found by the ratio of input distance to output distance. IMA = s in s out The actual mechanical advantage (AMA) of a simple machine is the ratio of output force to input force. This can be thought of as the produced by using the machine. AMA = F out F in The efficiency (ε) of a machine is the ratio of energy output to energy input. It is also the ratio of AMA to IMA. ε = W out W in = AMA IMA = F outs out F in s in

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