Simple Machines

Principles of Simple Machines

A machine is meant to simply transmit mechanical work from one part of a device to another. Since a machine produces force it also controls the direction and the motion of force, but it cannot create energy. A machine's ability to do work is measured by two factors: mechanical advantage and efficiency.

Mechanical Advantage:

In machines that transmit only mechanical energy, the ratio of the force exerted by the machine to the force applied to the machine is known as mechanical advantage. With mechanical advantage, the distance the load moved will only be a fraction of the distance where effort is applied. While machines can provide a mechanical advantage of greater than \( 1.0\) (and even less than \( 1.0\) if desired), no machine can do more mechanical work than the mechanical work that was put into it.

Efficiency:

The efficiency of a machine is just the ratio between the work it supplies and the work put into it. Even though friction can be decreased by oiling any sliding or rotating parts, all machines produce friction. Simple machines always have efficiencies of less than \( 1.0\) due to internal friction.

Energy Conservation:

If we ignore losses of energy due to friction, the work done on a simple machine would be the same as the work done by the machine to perform some sort of task. If work coming in equals work going out, then the machine is \( 100 \%\) efficient.

Types of Simple Machines

In everyday language, the term work can be used to describe a variety of concepts. However, in physics the term has a much more precise definition.

A machine makes work easier by one or more of the following functions:

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• transferring a force from one place to another
• changing the direction of a force
• increasing the magnitude of a force
• increasing the distance or speed of a force

Six classic types of simple machines make work easier and have few or no moving parts: wedge, screw, pulley, inclined plane, lever, axle, and a wheel (gear).

Let's read more about each of these simple machines.

Wedge

A wedge is a simple machine used to split a material. A wedge is a triangular-shaped tool and is a portable inclined plane. The wedge can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. Wedges can be seen in many cutting tools such as a knife, axe, or scissors. Using the example of an axe, when you place the thin end of the wedge onto a log, you can hit it with a hammer. The wedge changes the direction of the force and pushes the log apart.

Keep in mind that the longer and thinner or sharper a wedge is, the more efficiently it works. That means the mechanical advantage would be higher as well. This is because the mechanical advantage of a wedge is given by the ratio of the length of its slope to its width. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle.

Different types of wedges are used to make work easier in many ways. For example, in prehistoric times wedges were used to make spears for hunting. In the present day, wedges are used in modern cars and jets. Have you ever noticed pointy noses on fast cars, trains, or speedboats? These wedges 'cut through' the air reducing air resistance, making the machine go faster.

Screw

A screw is an inclined plane wrapped around a center rod. It is usually a circular cylindrical member with a continuous helical rib, used either as a fastener or as a force and motion modifier. A screw is a mechanism that converts rotational motion to linear motion and torque to a linear force. Screws are commonly used to fasten objects or hold things together. Some good examples of screws are bolts, screws, bottle tops, guitar tuners, light bulbs, faucet taps, and cork openers.

You might notice when using a screw that it is easier to drive it into an object if the thread spacing is smaller; it takes less effort but more turns. Or, if the spaces between the threads are wider, it is harder to drill a screw into an object. It takes more effort but fewer turns. The mechanical advantage of a screw depends on the space between the threads and the thickness of the screw. This is because the closer the threads are, the greater the mechanical advantage.

Pulley

A pulley is a wheel with a groove and a rope in the groove. The groove helps to keep the rope in place when the pulley is used to lift or lower heavy objects. The downward force turns the wheel with the rope and pulls the load upwards at the other end. A pulley can also move things from low to higher areas. A pulley has a wheel that allows you to change the direction of a force. As you pull down on the rope, the wheel turns and whatever is attached to the other end goes up. You may know of a pulley system from seeing a flag hoisted on a pole. There are three types of pulleys: fixed compound and moveable. Each pulley system depends on how the wheel and ropes are combined. Elevators, cargo lifts, wells, and exercise equipment also use pulleys to function.

Inclined Plane

An inclined plane is a simple machine with no moving parts. An even-sloping surface makes it easier for us to move objects to higher or lower surfaces than if we lifted the objects directly. An inclined plane can also help you move heavy objects. You may know of an inclined plane as a ramp or a roof.

There is a greater mechanical advantage if the slope is not steep because less force will be needed to move an object up or down the slope.

Lever as a Simple Machine

A lever is a rigid bar resting on a pivot at a fixed place called the fulcrum. A seesaw is an excellent example of a lever.

Fig. 1 - A see-saw is an example of a simple machine.

The parts of a lever include:

1. Fulcrum: the point at which the lever rests and pivots.
2. Effort (input force): characterized by the amount of work the operator does and is calculated as the force used multiplied by the distance over which the force is used.
3. Load (output force): the object being moved or lifted, sometimes referred to as resistance.

In order to lift the weight on the left (the load) a downward effort force is required on the right side of the lever. The amount of effort force required to raise the load depends on where the force is applied. The task will be easiest if the effort force is applied as far from the fulcrum as possible.

Fig. 2 - An example of a load and effort simple machine.

Torques are involved in levers since there is rotation about a pivot point. Distances from the physical pivot of the lever are crucial, and we can obtain a useful expression for the MA in terms of these distances.

Classes of Levers

There are three classes of levers: 1st class, 2nd class, and 3rd class.

1st class levers

The fulcrum is placed between the effort and the load. These types of levers may or may not provide a mechanical advantage, depending on the location of the effort force. If the effort is applied farther from the fulcrum than the load, you achieve a mechanical advantage (force multiplier). However, if you apply the effort force closer to the fulcrum than the load, you are working at a mechanical disadvantage (or an advantage < 1).

2nd class levers

The load is always between the effort and the fulcrum. These types of levers produce a mechanical advantage (MA >1) because the effort force is applied farther from the fulcrum than the load. The effort force and load are always on the same side of the fulcrum.

3rd class levers

The effort is between the load and the fulcrum. These types of levers give a mechanical disadvantage but allow a wide range of motion of the load. Many hydraulic systems use a 3rd class lever because the output piston can only move a short distance.

When classifying the lever, it is best to associate them with what is located in the middle. An easy trick is to remember: 1-2-3, F-L-E. By remembering this simple trick, it will tell one what is located in the middle.

For instance, in a second-class lever, the load is positioned in the middle of the system. Levers provide a mechanical advantage. Ideal mechanical advantage is defined as how many times the machine will multiply the effort force. Mechanical advantage is a ratio of the input side (effort) and output side (load) of the machine. These values are the distance the fulcrum is from the effort \( (I)\) and the distance the fulcrum is from the load \( O)\). Ideal mechanical advantage is a factor by which a machine changes (increases or decreases) the input force.

$$\mathrm{I M A}=I / O$$

When the input force (effort) is applied at a greater distance from the fulcrum than the load's location, the mechanical advantage is magnified. In addition to distance, \(\mathrm{IMO}\) can also be related to force through the following formula.

$$F_L=(\mathrm{I M A})F_e,$$

where, \( F_L\) is the load the operator can lift, aka the load or output force, and \(F_E\) is the effort force.

Gear as a Simple Machine

Fig. 5 - A gear system is a simple machine.

A gear is a wheel and axle type of simple machine that has teeth along the wheel. Often they are used in combination with one another and change the direction of forces. The size of the gear determines the speed it rotates. Gears are used in machines to increase force or speed.

If you have ever tried to ride a bicycle up a steep hill, you probably have an understanding of how gears work. Getting up the hill is practically impossible unless you have the right gear to increase your climbing force. Likewise, if you are riding your bicycle, you know that going straight, fast, or uphill would all use a specific force to generate more speed or send the bicycle off in another direction. This is all related to the gear your bicycle is in.

Gears are brilliantly helpful, but there's one thing we should consider. If a gear gives you more force, it must also turn the wheel slower. If it spins faster, it has to give you less force. That's why, when you're going uphill in low gear, you have to pedal vastly faster to go the same distance. When you're going along a straight path, gears give you more speed, but they decrease the force you're producing with the pedals in the same proportion. Gears are advantageous for machines of all kinds, not just bicycles. They're a simple way to generate speed or force. So, in physics, we say gears are simple machines.

Examples of Simple Machines

You might be wondering what some everyday examples of simple machines would look like. Take a look at the chart below with some examples of the different types of Simple Machines. Are there any examples that surprise you?

Let's work on a few problems for simple machines.