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Background information for simple machines

Can we help you? Below you will find some commonly asked questions about simple machines. You may also want to explore the other topics relating to our school program «Pulleys and Gears : Wonderful Machines»

What is a simple machine?

Machines are used to reduce the amount of force required to do work, such as lift a load, but the trade off is that you must apply this force over a greater distance.

Man has learned to use machines to help him do work - which in our case means to move things. Some machines, such as bicycles, are complex because they involve more than one simple machine.

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What are the two basic families of simple machines?

All simple machines are derived from either the inclined plane or the lever.

The six types of simple machines are:

  • the inclined plane
  • the wedge
  • the screw
  • the lever
  • the wheel and axle
  • the pulley
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Which machines belong to the inclined plane family?

The inclined plane

The word "inclined" means "at an angle". The word "plane" means "a flat surface". An inclined plane is a slope or a ramp. It can be any slanted surface used to raise a load from a lower level to a higher level. Examples of an inclined plane include: a ramp used by a workman to push a heavy load on wheels up into a truck, ramps for wheel chairs, ramps to load luggage onto a plane, an escalator. An inclined plane was used to move huge stones to build the Egyptian Pyramids.

Notice that all these inclined planes are stationary (with the exception of the stairs moving on an escalator). Inclined planes don't move! An inclined plane helps a person to move or raise heavy objects. An inclined plane enables a load to be lifted with less force, but the distance over which it moves is greater.

In other words, when an inclined plane is used, less force is required to move the resisting weight up the slanted surface than to lift it up vertically. However the amount of work remains the same since:

    Work = Force x distance.

    W = Fd

The wedge - two inclined planes put back to back.

It is not really a separate type of machine, as the principle involved is identical to that of the inclined plane.

Some examples of wedges include: chisels, axes, knives, saws (small wedges), a splitting wedge, a doorstop, a plow, the hull of a boat

The screw - the circular version of the inclined plane, though it must move to work.

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Which machines belong to the lever family?

The lever - a bar that turns on a point, called a fulcrum.

The wheel and axle - a circular lever, whose fulcrum (pivot point) is an axle.

The pulley - another circular lever, but the pulley wheel rotates freely on the axle.

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Why does an inclined plane make work easier?

Principle of the Inclined Plane

    W = Fd (Force x distance)

As with all simple machines, the inclined plane can be used to trade increased distance for decreased force or effort. The force is applied in a different direction to that in which movement takes place.

Can you get something for nothing?

No!

The steepness of the inclined plane is a key factor. If a person uses a longer board to make the inclined plane, he or she will need less force to move the object up the ramp. If a shorter board is used (the angle of the slope is steeper), more force is required but the distance over which it must be applied is less.

For an object resting on an inclined plane, the vertical force of gravity acting on it is split into two smaller forces; one perpendicular to the plane, and one parallel to the plane. It is only the parallel force which needs to be counteracted by pushing (and, of course, friction, though we are ignoring that for this exercise). The slope provides "mechanical advantage" as a simple machine.

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How does the wedge work?

A double wedge is made up of two inclined planes back to back. You find a double wedge on an axe blade. Single wedges resemble an inclined plane, because they have only one sloping surface. A doorstop is a single wedge. Remember that the inclined plane does not move.

Wedges can be used in several ways:

  • Wedges can help you grip things to be lifted. Pushing one under an object provides a space for your fingers. The longer the wedge and the smaller the angle of slope, the less the force needed, but the wedge must be pushed in a greater distance.
  • Wedges can also be used to tighten or hold things in place, for example, a wedge peg to hold a bench together, or a doorstop.
  • Wedges are mostly used to push things apart, for example, pounding a nail into a block of wood. Other examples are a chisel, cutting tools, an axe (also a lever), a can opener (also a lever), plow blade, and the bow of a boat or ship.

Principle of the Wedge

The purpose or advantage of the wedge is to change the direction of the applied force. When the force is applied downward on a wedge, it is able to push outward in two directions.

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A special form of the inclined plane - The screw

A screw is an inclined plane wrapped around a cylinder. The inclined plane forms ridges in a spiral along the cylinder. These ridges are called the threads of the screw. The distance between the threads is called "the pitch" of the screw.

The Principle of the Screw

It would be impossible to completely insert a screw into a piece of wood without using a screwdriver. Thus you trade the extra distance moved as you turn the handle of the screwdriver, for the reduced force required to turn the screw. As with the inclined plane, force is applied in a direction different from the movement of the load.

The screw also resists pulling out much better than a nail and therefore provides a stronger joint.

The principle of the screw can be easily understood by cutting a right-angled triangle out of paper. Colour the triangle's hypotenuse. Wrap it around a pencil.

The triangle's hypotenuse becomes the inclined plane or threads of the screw. A screw depends on another simple machine, a screwdriver (a lever), for its operation. A screw works with rotating movement, which is provided by a lever.

When the lever arm makes a full turn, the screw is moved a distance equal to the pitch, or the gap between adjacent threads.

A screw's mechanical advantage is the ratio of two dimensions: the length of the lever that turns it, and the distance between the threads. Thus, a screw can function in two ways. It can raise weights (liquids or solids), or it can press or fasten objects.

Archimedes' Screw

One of the first screw machines, invented in the third century B.C., is commonly attributed to the Greek geometer, Archimedes. It was to irrigate the fields, and to pump water out of a ship's hold. This machine had a watertight cylinder enclosing a spiral running from end to end, with its lower end immersed in water. The machine was turned by hand, and the water collected in the rotating spiral blades. These blades appeared to rise, as the screw turned. The water poured out a hole in the top of the cylinder.

Some modern examples of screws include:

  1. To move or raise liquids or solids - a snowblower, a ship or airplane propeller, a worm gear, a corkscrew, a jack screw, a pig feeder, a grain thresher, a meat grinder, a piano stool, a corn sheller.
  2. To press or fasten objects - book binding press, a vise, a screw hook, nut and bolt, an auger (hand drill), a monkey wrench, an ordinary screw, a jar lid, and a screw press for printing.

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Let's examine the lever

A lever consists of a rigid arm, which is free to turn about a fixed point called the fulcrum. The fulcrum is a pivot point. The effort force (push or pull) is exerted upon one lever arm, and the other lever arm will go up or down in the opposite direction. The resisting weight (the load) is exerted upon the lever arm, which tends to move the lever in the opposite direction to the applied force.

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Principles of the lever family

With levers, the force is applied at a different point from the load.

The closer the fulcrum to the load, the less force needed to lift the load. The force will move a greater distance, and the load will move a shorter distance.

The closer the fulcrum to the force, the greater the force needed to lift the load. The force will move a shorter distance, and the load will move a greater distance.

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Classes of levers

Levers are divided into three classes, according to the way the load and force arms are arranged around the fulcrum.

First Class Lever

When the fulcrum lies between the force arm and the lever arm, the lever is described as a first class lever. In fact many of us are familiar with this type of lever. It is the classic teeter-totter example.

When the fulcrum is midway between the force and the load, there is no change in force, speed or distance.

Other first class levers include: a car jack, a pair of pliers, a pair of scissors, a water pump, a balance or pair of weigh scales, a crowbar, a claw of a hammer taking out a nail, or a lever with a rock as its fulcrum trying to lift another rock.

Second Class Lever

In the second class lever, the load arm lies between the fulcrum and the force arm. A good example of this type of lever is the wheelbarrow. The axle of the wheel serves as the fulcrum, the handles are the force arm, and the load is carried between the two in the bucket part of the wheel barrow.

In the second class lever, the fulcrum is usually closer to the load, which reduces the force needed to accomplish the work.

Some other examples of the second class lever are: a pair of nutcrackers, and a bottle opener.

Third Class Lever

In this class of levers, the force arm lies between the fulcrum and the load arm. Because of this arrangement, a relatively large force is required to move the load. This is offset by the fact that it is possible to produce movement of the load over a long distance with a relatively small movement of the force arm. Think of a fishing rod! Because of this relationship, we often employ this class of lever when we wish to produce large movements of a small load, or to transfer relatively low speed of the force arm to high speed of the load arm. When a hockey stick or a baseball bat is swung, a third class lever is in effect. The elbow acts as a fulcrum in both cases and the hands provide the force (hence the lower arm becomes part of the lever). The load (i.e. the puck or the ball) is moved at the end of the stick or bat.

In a third class lever there is usually a loss in force needed to accomplish the work, but a gain in speed or distance.

Example of third class levers are: a fishing pole, a pair of tweezers, an arm lifting a weight, a pair of calipers, a person using a broom, a hockey stick, a tennis racket, a spade, or a shovel.

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What is a wheel and axle?

The wheel and axle is a first class lever in which the fulcrum has been replaced by an axle and the arms have been repeated around the axle to make up the spokes or disk of the wheel. This allows the lever to rotate through 360º instead of the limited rotation in the teeter-totter application.

However, it is important to differentiate between a wheel used simply as a roller to counteract friction (i.e. the front wheel of a bicycle), and the wheel and axle where a small amount of force is applied to the wheel which moves the axle with greater force (i.e. the back wheel of a bicycle driven by pedals/gears). With the roller, the force that moves the object is often not applied directly to the wheel.

Early man discovered that several logs under a heavy object helped reduce friction, when moving an object. This "roller" method was awkward. The wheel evolved from one solid round of wood, to a wheel that is built up with a number of small pieces (spokes, rim etc.).

Some examples of a wheel and axle are: a windlass, a capstan, a water wheel, a windmill, gears, doorknobs, faucet handles, and steering wheels.

The Windlass

The windlass is like the rope and crank of a wishing well. A rope on an axle is turned by a crank (wheel), to raise the bucket of water. The windlass originated several thousands of years ago with the Babylonians. The rope is wound up onto a cylindrical-shaped wheel. In the past, the windlass was used to haul ore from mines, or to open and close heavy gates of water canals. They were also used on boats to hoist sails and lift anchors.

The Capstan

A capstan is similar to a windlass. It is used to raise heavy anchors on large ships. A capstan is a revolving barrel with a vertical axis. An early version was operated by men walking around it, pushing on horizontal bars that were attached to the top of the wooden barrel. Today, motors drive the capstan. The revolving spindle on a tape recorder is also a capstan.

The Water Wheel and the Windmill

The Greeks invented the "water wheel", a wheel and axle pushed by the moving water of a river. It is said that, in the first century B.C., a Roman engineer, named Vituvius, designed the first practical water wheel. Buckets were placed on the rim of the wheel and water falling into the buckets caused the wheel to turn.

Windmills haven't been around as long as water wheels but they were built on similar principles and for similar reasons. For centuries windmills resembled tall fans with four to six arms. Both water wheels and windmills run on either horizontal or vertical gear systems.

Water wheels and windmills have been used for grinding grain, sawing lumber, or as a source of power in the manufacture of clothing, metal and paper.

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The gear - a special form of lever

Gears are wheels with teeth that can be used to gain force or speed or change direction.

When one gear drives another, the two gears turn in the opposite direction. If it is required that they turn in the same direction, a third gear called an "idler gear" is interposed between them.

The size and number of teeth on a gear determine the kind of work it can do. A force on a large gear will cause a small gear to turn faster, but with less force. A force on a small gear will turn the large gear more slowly, but it will have a greater force. The distance between the teeth of the gear is called the "pitch".

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The Pulley

A pulley is a wheel with a groove that allows a rope, belt or chain to ride securely on it.

A pulley is a circular lever, with the wheel rotating freely on the axle. A fixed pulley is fastened to one spot, and does not move around. It provides no gain in force, distance or speed, but it changes the direction of the force. A fixed pulley acts as a first class lever. The fulcrum is the axle (the point at which the pulley is supported).

The force arm is the radius of the pulley - that is, the distance from the fulcrum (axle) to the side of the rope on which we pull. The load arm is also the radius of the pulley - the distance from the fulcrum (axle) to the load-carrying side of the rope. Examples of fixed pulleys can be seen on flag poles, drapes, or on a sail mast. In each case, the pulley changes the direction of the applied force, to enable work to be accomplished.

A movable pulley moves along a rope or wire. It provides a gain in force, but a loss in distance. (You have to pull the rope twice as far!) A movable pulley works like a turning second class lever. The fulcrum is at one rim of the pulley wheel, the load is at the axle, and the force is at the other rim of the pulley wheel.

Why do moving pulleys make lifting easier?

More sections of rope are supporting the weight. This is like having someone help you carry something heavy. The more help you have, the lighter the load seems to be.

Mechanical advantage is determined by the number of supporting ropes of the movable pulley(s).

A compound pulley, also called a block and tackle, is a combination of a fixed and a movable pulley. This type of pulley changes direction, and yields a gain in force at the same time.

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What does "work" mean in science?

The simple machines all require human energy in order to work. What does work mean? "Work" has a special meaning in science. "Work" is only done when something is moved. For example, when you push on the locomotive in the Museum, you actually are not doing work, because you cannot move it.

Work consists of two parts. One is the amount of force (push or pull) needed to do the work. The other is the distance over which the force is applied.

The formula for work is: Work = Force X Distance. Work is measured in joules. Force is the pull or the push on an object, resulting in its movement. Force is measured in newtons. Distance is the space the object moves. It is measured in metres. Thus, the work done (in joules) is the force moved (in newtons) multiplied by the distance moved (in metres).

When we say a machine makes it easier for us to do work, we mean that it requires less force to accomplish the same amount of work. Apart from allowing us to increase the distance over which we apply the smaller force, machines may also allow us to change the direction of an applied force.

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What is "mechanical advantage"?

Mechanical Advantage is the ratio of the existing weight or load to the acting force; or, the ratio of the distance through which the force is exerted to the distance the weight is raised. For example, a machine has a mechanical advantage of 5 if an applied force of 1 kg can counterbalance a weight of 5 kg.

Mechanical Advantage = W
F
= Sf
Sw
where: W is the weight being raised
F is the acting force
Sf is the distance the acting force moves
Sw is the distance the resisting weight or load is raised

The acting force times the distance it moves equals the work put into the machine. This work is called the input force. The resisting weight times the distance it moves equals the work accomplished by the machine. This work is called the output force.

Here the mechanical advantage is determined by the number of supporting ropes of the movable pulley.

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