In physics, a simple machine is any device that requires the application of only one force in order to perform work. Work is the product of the force applied and the distance moved due to the force. Most authorities list six kinds of simple machines: levers, pulleys, wheels and axles, inclined planes, wedges, and screws. One can argue, however, that these six machines are not entirely different from each other. Pulleys and wheels and axles, for example, are really special kinds of levers, and wedges and screws are special kinds of inclined planes.
A lever is a simple machine that consists of a rigid bar supported at one point, known as the fulcrum. A force called the effort force is applied at one point on the lever in order to move an object, known as the resistance force, located at some other point on the lever. A common example of the lever is the crow bar used to move a heavy object such as a rock. To use the crow bar, one end is placed under the bar, which is supported at some point (the fulcrum) close to the rock. A person then applies a force at the opposite end of the crow bar to lift the rock. A lever of the type described here is a first-class lever because the fulcrum is placed between the applied force (the effort force) and the object to be moved (the resistance force).
The effectiveness of the lever as a machine depends on two factors: the forces applied at each end and the distance of each force from the fulcrum. The farther a person stands from the fulcrum, the more his or her force on the lever is magnified. Suppose that the rock to be lifted is only one foot from the fulcrum and the person trying to lift the rock stands 2 yd (1.8 m) from the fulcrum. Then, the person's force is magnified by a factor of six. If he or she pushes down with a force of 30 lb (13.5 kg), the object that is lifted can be as heavy as 180 (6 x 30) lb (81 kg).
Two other types of levers exist. In one, called a second-class lever, the resistance force lies between the Page 2672 | Top of Articleeffort force and the fulcrum. A nutcracker is an example of a second-class lever. The fulcrum in the nutcracker is at one end, where the two metal rods of the device are hinged together. The effort force is applied at the opposite ends of the rods, and the resistance force, the nut to be cracked open, lies in the middle.
In a third-class lever, the effort force lies between the resistance force and the fulcrum. Some kinds of garden tools are examples of third-class levers. When a person uses a shovel, for example, one holds the handle end steady to act as the fulcrum, while using the other hand to pull up on a load of dirt. The second hand is the effort force, and the dirt being picked up is the resistance force. The effort applied by the second hand lies between the resistance force (the dirt) and the fulcrum (the first hand).
The term mechanical advantage is used to describe how effectively a simple machine works. Mechanical advantage is defined as the resistance force moved divided by the effort force used. In the aforementioned lever example, for example, a person pushing with a force of 30 lb (13.5 kg) was able to move an object that weighed 180 lb (81 kg). So, the mechanical advantage of the lever in that example was 180 lb divided by 30 lb, or 6.
The mechanical advantage described here is really the theoretical mechanical advantage of a machine. In actual practice, the mechanical advantage is always less than what a person might calculate. The main reason for this difference is resistance. When a person does work with a machine, there is always some resistance to that work. For example, a mathematician can calculate the theoretical mechanical advantage of a screw (a kind of simple machine) that is being forced into a piece of wood by a screwdriver. The actual mechanical advantage is much less than what is calculated because friction must be overcome in driving the screw into the wood.
Sometimes the mechanical advantage of a machine is less than one. That is, a person has to put in more force than the machine can move. Class three levers are examples of such machines. A person exerts more force on a class three lever than the lever can move. The purpose of a class three lever, therefore, is not to magnify the amount of force that can be moved, but to magnify the distance the force is being moved.
As an example of this kind of lever, imagine a person who is fishing with a long fishing rod. The person will exert a much larger force to take a fish out of the water than the fish itself weighs. The advantage of the fishing pole, however, is that it moves the fish a large distance, from the water to the boat or the shore.
A pulley is a simple machine consisting of a grooved wheel through which a rope runs. The pulley can be thought of as a kind of lever if one thinks of the grooved wheel as the fulcrum of the lever. Then the effort force is the force applied on one end of the pulley rope, and the resistance force is the weight that is lifted at the opposite end of the pulley rope.
In the simplest form of a pulley, the grooved wheel is attached to some immovable object, such as a ceiling or beam. When a person pulls down on one end of the pulley rope, an object at the opposite end of the rope is raised. In a fixed pulley of this design, the mechanical advantage is one. That is, a person can lift a weight equal to the force applied. The advantage of the pulley is one of direction. An object can be made to move upward or downward with such a pulley. Venetian blinds are a simple example of the fixed pulley.
In a movable pulley, one end of the pulley rope is attached to a stationary object (such as a ceiling or beam), and the grooved wheel is free to move along the rope. When a person lifts on the free end of the rope, the grooved wheel and any attached weight slides upward on the rope. The mechanical advantage of this kind of pulley is two. That is, a person can lift twice as much weight as the force applied on the free end of the pulley rope.
More complex pulley systems can also be designed. For example, one grooved wheel can be attached to a stationary object, and a second movable pulley can be attached to the pulley rope. When a person pulls on the free end of the pulley rope, a weight attached to the movable pulley can be moved upward with a mechanical advantage of two. In general, in more complicated pulley systems, the mechanical advantage of the pulley is equal to the number of ropes that hold up the weight to be lifted. Combinations of fixed and movable pulleys are also known as a block and tackle. Some blocks and tackles have mechanical advantages high enough to allow a single person to lift weights as heavy as that of an automobile.
Wheel and axle
A second variation of the lever is the simple machine known as a wheel and axle. A wheel and axle consists of two circular pieces of different sizes attached to each other. The larger circular piece is the wheel in the system, and the smaller circular piece is the axle. One of the circular pieces can be considered as the effort arm of the lever and the second, the resistance arm. The place at which the two pieces is joined is the fulcrum of the system.
Some examples of the wheel and axle include a door knob, a screwdriver, an egg beater, a water wheel, the steering wheel of an automobile, and the crank used to raise a bucket of water from a well. When the wheel in a wheel and axle machine is turned, so is the axle, and vice versa. For example, when someone turn the handle of a screwdriver, the edge that fits into the screw head turns at the same time.
The mechanical advantage of a wheel and axle machine can be found by dividing the radius of the wheel by the radius of the axle. For example, suppose that the crank on a water well turns through a radius of 2 ft (61 cm) and the radius of the axle around which the rope is wrapped is 4 in (10 cm). Then, the mechanical advantage of this wheel and axle system is 2 ft divided by 4 in, or 6.
An inclined plane is any sloping surface. Many people have used an inclined plane at one time or another when they tried to push a wheelbarrow or a dolly up a sloping board into a truck. One major difference between an inclined plane and a lever is that motion always takes place with the latter, but not with the former.
The primary advantage of using an inclined plane is that it takes less effort to push an object up an inclined plane than it does to lift the same object through the same vertical difference. Just compare how difficult it might be to lift a can that weighs 10 lb (4.5 kg) straight up into a truck compared to how difficult it would be to push the same can up a sloping board into the truck.
The mechanical advantage of an inclined plane can be found by dividing the length of the plane by its height. In the preceding example, suppose that the sloping board is 10 ft (3 m) long and 2 ft (61 cm) high. Then, the mechanical advantage of the inclined plane would be 10/2, or 5. A person could move the ten pound weight into the truck using a force only one-fifth as great as if the can were lifted directly into the truck.
A wedge is an inclined plane that can be moved. Chisels, knives, hatches, carpenter's planes, and axes are all examples of a wedge. Wedges can have only one sloping plane, as in a carpenter's plane, or they can have two, as in a knife blade. The mechanical advantage of the wedge is calculated in the same way as with an inclined plane by dividing the length of the wedge by its width at the thickest edge.
A screw can be considered to be an inclined plane that has been wrapped around some central axis. A person can see this relationship by making an inclined plane out of paper and, then, wrapping the paper around a pencil. The spiral shaped form that you make is a screw.
Screws can be used in two major ways. First, they can be used to hold things together. Some simple examples include wood and metal screws and the screws on jars and bottles and their tops. Screws can also be used to apply force on objects. The screws found in vises, presses, clamps, monkey wrenches, brace and bits, and corkscrews are some examples of this application.
The screw acts as a simple machine when an effort force is applied to the larger circumference of the screw. For example, a person might apply the effort force to a wood screw by turning a screwdriver. That force is then transmitted down the spiral part of the screw called the thread to the tip of the screw. The movement of the screw tip into the wood is the resistance force in this machine. Each complete turn of the screwdriver produces a movement of only one thread of the screw tip into the wood. This distance between two adjacent threads is called the pitch.
The mechanical advantage of a screw can be found by dividing the circumference of the screw by its pitch. For example, suppose that a carpenter is working with screws whose heads have a circumference of 1 in (2.54 cm) and a pitch of 1/8 in (0.33 cm). Then the mechanical advantage of these screws is 1 divided by 1/8, or 8. The carpenter magnifies his or her efforts by a factor of 8 in driving the screw into a piece of wood.
In many instances, the combination of two or more simple machines achieves results that cannot be achieved Page 2674 | Top of Articleby a simple machine alone. Such combinations are known as compound machines. An example of a compound machine is the common garden hoe. The handle of the hoe is a lever, while the blade that cuts into the ground is a wedge. Machines with many simple machines combined with each other—such as typewriters, bicycles, and automobiles—are sometimes referred to as complex machines.
Ardley, Neil, and David Macaulay. The Way Things Work Now. Boston: Houghton Mifflin Harcourt, 2016.
Tiner, John Hudson. Exploring the World of Physics: From Simple Machines to Nuclear Energy. Green Forest, AR: Master Books, 2006.
Live Science. “Six Simple Machines: Making Work Easier.” https://www.livescience.com/49106-simple-machines.html (accessed May 18, 2020).
David E. Newton