Ребе topic simple machines. Методическая разработка занятия по английскому языку на тему "Машины и работа" (3 курс)

A screwdriver is used to pry the lid off a can of paint. What type of lever is the screwdriver in this instance? 1st Class Lever 2nd Class Lever 3rd Class Lever It’s actually acting as an inclined plane. 10

12 3.0 8.3 25 75 10

29 1.7 3.5 28 350 10

Participant Scores 12 Jacob Joey Daniel David Nicole B.

A single pulley is used to hoist a safe with a mass of 45. 0 kg
A single pulley is used to hoist a safe with a mass of 45.0 kg. If the machine is 100% efficient, what effort force will be required to hoist the safe? 45.0 N 90.0 N 205 N 266 N 441 N 10

A snow shovel is an example of which type of lever? (Hint: The handle of the shovel is the fulcrum.) 1st Class 2nd Class 3rd Class 10

How long must an inclined plane be to push a 100 kg object to a height of 2.0 meters using a force of 200 N? Friction can be ignored. 2.0 m 9.8 m 50 m 100 m 200 m 400 m 10

A wheel and axle machine requires an effort force of 5.0 N to lift a load with a mass of 5.1 kg. If the machine is ideal and has a wheel radius of 12 cm, what is the radius of the axle? 1.0 cm 1.2 cm 5.0 cm 10 cm 1.2 m 2.4 m 10

Participant Scores 28 Jacob Joey Daniel David Mackenzie

20 N 25 N 196 N 245 N 1960 N Answer Now 10

What force will be required to push a 500 N box to a height of 2.50 meters on a ramp that is 10.0 meters long and 85% efficient? 4.00 N 50.0 N 106 125 N 147 N 10

1 2 3 4 5 10

0.50 1.00 1.50 2.00 2.50 Answer Now 10

Participant Scores 44 Jacob Mackenzie 39 Nicole F. Joey Daniel

A ramp is 12 meters long and 3.0 meters high. It takes 145 N of force to push a 400 N crate up the ramp. Determine the efficiency of the ramp. .36 % .69 % 3.0 % 8.2 % 36 % 69 % 145 % 10

An object is placed 1. 75 meters from the fulcrum of a lever
An object is placed 1.75 meters from the fulcrum of a lever. The effort force is 0.50 meters from the fulcrum. What is the actual mechanical advantage if the lever is 95% efficient? .271 .286 .301 3.33 3.50 3.68 Answer Now 10

20% 31% 69% 80% 87% 96% Answer Now 10

Participant Scores 56 Jacob Mackenzie 51 Nicole F. Joey Daniel

A certain ramp is 10 meters long and is 50% efficient
A certain ramp is 10 meters long and is 50% efficient. It requires 25 N of force to push a 50 N crate up the ramp. How tall is the ramp? 1.0 m 2.0 m 2.5 m 3.5 m 4.0 m 5.0 m 22
Participant 1 Participant 2 Participant 3 Participant 4 Participant 5 Participant 6 Participant 7 Participant 8 Participant 9 Participant 10

UXL Encyclopedia of Science
COPYRIGHT 2002 The Gale Group, Inc.

Machines, simple

A simple machine is a device for doing work that has only one part. Simple machines redirect or change the size of forces, allowing people to do work with less muscle effort and greater speed, thus making their work easier. There are six kinds of simple machines: the lever, the pulley, the wheel and axle , the inclined plane , the wedge, and the screw.

Everyday work

We all do work in our daily lives and we all use simple machines every day. Work as defined by science is force acting upon an object in order to move it across a distance. So scientifically, whenever we push, pull, or cause something to move by using a force, we are performing work. A machine is basically a tool used to make this work easier, and a simple machine is among the simplest tools we can use. Therefore, from a scientific standpoint, we are doing work when we open a can of paint with a screwdriver, use a spade to pull out weeds, slide boxes down a ramp, or go up and down on a see-saw. In each of these examples we are using a simple machine that allows us to achieve our goal with less muscle effort or in a shorter amount of time.

Earliest simple machines

This idea of doing something in a better or easier way or of using less of our own muscle power has always been a goal of humans. Probably from the beginning of human history, anyone who ever had a job to do would eventually look for a way to do it better, quicker, and easier. Most people try to make a physical job easier rather than harder to do. In fact, one of our human predecessors is called Homo habilis, which means "handy man" or "capable man." This early version of our human ancestors was given that name because, although not quite fully human, it had a large enough brain to understand the idea of a tool, as well as hands with fingers and thumbs that were capable of making and using a tool. Therefore, the first simple machine was probably a strong stick (the lever) that our ancestor used to move a heavy object, or perhaps it was a sharp rock (the wedge) used to scrape an animal skin, or something else equally simple but effective. Other early examples might be a rolling log, which is a primitive form of the wheel and axle , and a sloping hill, which is a natural inclined plane . There is evidence throughout all early civilizations that humans used simple machines to satisfy their needs and to modify their environment.

Words to Know

Compound machine: A machine consisting of two or more simple machines.

Effort force: The force applied to a machine.

Fulcrum: The point or support on which a lever turns.

Resistance force: The force exerted by a machine.

Work: Transfer of energy by a force acting to move matter.

The beauty of simple machines is seen in the way they are used as extensions of our own muscles, as well as in how they can redirect or magnify the strength and force of an individual. They do this by increasing the efficiency of our work, as well as by what is called a mechanical advantage. A mechanical advantage occurs when a simple machine takes a small "input" force (our own muscle power) and increases the magnitude of the "output" force. A good example of this is when a person uses a small input force on a jack handle and produces an output force large enough to easily lift one end of an automobile. The efficiency and advantage produced by such a simple device can be amazing, and it was with such simple machines that the rock statues of Easter Island , the stone pillars of Stonehenge, and the Great Pyramids of Egypt were constructed. Some of the known accomplishments of these early users of simple machines are truly amazing. For example, we have evidence that the builders of the pyramids moved limestone blocks weighing between 2 and 70 tons (1.8 and 63.5 metric tons) hundreds of miles, and that they built ramps over 1 mile (1.6 kilometers) long.

Trade-offs of simple machines

One of the keys to understanding how a simple machine makes things easier is to realize that the amount of work a machine can do is equal to the force used, multiplied by the distance that the machine moves or lifts the object. In other words, we can multiply the force we are able to exert if we increase the distance. For example, the longer the inclined plane— which is basically a ramp— the smaller the force needed to move an object. Picture having to lift a heavy box straight up off the ground and place it on a high self. If the box is too heavy for us to pick up, we can build a ramp (an inclined plane) and push it up. Common sense tells us that the steeper (or shorter) the ramp, the harder it is to push the object to the top. Yet the longer (and less steep) it is, the easier it is to move the box, little by little. Therefore, if we are not in a hurry (like the pyramid builders), we can take our time and push it slowly up the long ramp to the top of the shelf.

Understanding this allows us also to understand that simple machines involve what is called a "trade-off." The trade-off, or the something that is given up in order to get something else, is the increase in distance. So although we have to use less force to move a heavy object up a ramp, we have increased the distance we have to move it (because a ramp is not the shortest distance between two points). Most primitive people were happy to make this trade-off since it often meant being able to move something that they otherwise could not have moved.

Today, most machines are complicated and use several different elements like ball bearings or gears to do their work. However, when we look at them closely and understand their parts, we usually see that despite their complexity they are basically just two or more simple machines working together. These are called compound machines. Although some people say that there are less than six simple machines (since a wedge can be considered an inclined plane that is moving, or a pulley is a lever that rotates around a fixed point), most authorities agree that there are in fact six types of simple machines.

Lever

A lever is a stiff bar or rod that rests on a support called a fulcrum (pronounced FULL-krum) and which lifts or moves something. This may be one of the earliest simple machines, because any large, strong stick would have worked as a lever. Pick up a stick, wedge it under one edge of a rock, and push down and you have used a lever. Downward motion on one end results in upward motion on the other. Anything that pries something loose is also a lever, such as a crow bar or the claw end of a hammer. There are three types or classes of levers. A first-class lever has the fulcrum or pivot point located near the middle of the tool and what it is moving (called the resistance force). A pair of scissors and a seesaw are good examples. A second-class lever has the resistance force located between the fulcrum and the end of the lever where the effort force is being made. Typical examples of this are a wheelbarrow, nutcracker, and a bottle opener. A third-class lever has the effort force being applied between the fulcrum and the resistance force. Tweezers, ice tongs, and shovels are good examples. When you use a shovel, you hold one end steady to act as a fulcrum, and you use your 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 your second hand lies between the resistance force (dirt) and the fulcrum (your first hand).

Pulley

A pulley consists of a grooved wheel that turns freely in a frame called a block through which a rope runs. In some ways, it is a variation of a wheel and axle, but instead of rotating an axle, the wheel rotates a rope or cord. In its simplest form, a pulley"s grooved wheel is attached to some immovable object, like a ceiling or a beam. When a person pulls down on one end of the rope, an object at the opposite end is raised. A simple pulley gains nothing in force, speed, or distance. Instead, it only changes the direction of the force, as with a Venetian blind (up or down). Pulley systems can be movable and very complex, using two or more connected pulleys. This permits a heavy load to be lifted with less force, although over a longer distance.

Wheel and axle

The wheel and axle is actually a variation of the lever (since the center of the axle acts as the fulcrum). It may have been used as early as 3000 b.c., and like the lever, it is a very important simple machine. However, unlike the lever that can be rotated to pry an object loose or push a load along, a wheel and axle can move a load much farther. Since it consists of a large wheel rigidly attached to a small wheel (the axle or the shaft), when one part turns the other also does. Some examples of the wheel and axle are a door knob, a water wheel , an egg beater, and the wheels on a wagon, car, or bicycle. When force is applied to the wheel (thereby turning the axle), force is increased and distance and speed are decreased. When it is applied to the axle (turning the wheel), force is decreased and distance and speed are increased.

Inclined plane

An inclined plane is simply a sloping surface. It is used to make it easier to move a weight from a lower to a higher spot. It takes much less effort to push a wheel barrow load slowly up a gently sloping ramp than it does to pick it up and lift it to a higher spot. The trade-off is that the load must be moved a greater distance. Everyday examples are stairs, escalators, ladders, and a ship"s plank.

Wedge

A wedge is an inclined plane that moves and is used to increase force— either to separate something or to hold things together. With a wedge, the object or material remains in place while the wedge moves. A wedge can have a single sloping surface (like a door stop that holds a door tightly in place), or it can have two sloping surfaces or sides (like the wedge that splits a log in two). An axe or knife blade is a wedge, as is a chisel, plow, and even a nail.

Screw

A screw can be considered yet another form of an inclined plane, since it can be thought of as one that is wrapped in a spiral around a cylinder or post. In everyday life, screws are used to hold things together and to lift other things. When it is turned, a screw converts rotary (circular) motion into a forward or backward motion. Every screw has two parts: a body or post around which the inclined plane is twisted, and the thread (the spiraled inclined plane itself). Every screw has a thread, and if you look very closely at it, you will see that the threads form a tiny "ramp"

that runs from the tip to the top. Like nails, screws are used to hold things together, while a drill bit is used to make holes. Other examples of screws are airplane and boat propellers.

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.

Levers

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

effort 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).

Mechanical advantage

The term mechanical advantage is used to described how effectively a simple machine works. Mechanical advantage is defined as the resistance force moved divided by the effort force used. In the lever example above, 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.

Pulleys

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.

Inclined planes

KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compound machine

A machine consisting of two or more simple machines.

Effort force

The force applied to a machine.

Friction

A force caused by the movement of an object through liquid, gas, or against a second object that works to oppose the first object"s movement.

Mechanical advantage

A mathematical measure of the amount by which a machine magnifies the force put into the machine.

Resistance force

The force exerted by a machine.

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  You"re watching FreeSchool! Hi everyone! Today we"re going to talk about simple machines. A simple machine is a device that makes work easier by magnifying or changing the direction of a force. That means that simple machines allow someone to do the same work with less effort! Simple machines have been known since prehistoric times and were used to help build the amazing structures left behind by ancient cultures. The Greek philosopher Archimedes identified three simple machines more than 2,000 years ago: the lever, the pulley, and the screw. He discovered that a lever would create a mechanical advantage, which means that using a lever would allow a person to move something that would normally be too heavy for them to shift. Archimedes said that with a long enough lever and a place to rest it, a person could move the world. Over the next few centuries more simple machines were recognized but it was less than 450 years ago that the last of the simple machines, the inclined plane, was identified. There are six types of simple machines: the Lever, the Wheel and Axle, the Pulley, the Inclined plane, the Wedge, and the Screw. Pulleys and Wheel and Axles are both a type of Lever. Wedges and Screws are both types of Inclined Planes. Each type of Simple Machine has a specific purpose and way they help do work. When speaking of simple machines, "work" means using energy to move an object across a distance. The further you have to move the object, the more energy it takes to move it. Let"s see how each type of simple machine helps do work. A LEVER is a tool like a bar or rod that sits and turns on a fixed support called a fulcrum. When you use a lever, you apply a small force over a long distance, and the lever converts it to a larger force over a shorter distance. Some examples of levers are seesaws, crowbars, and tweezers. A Wheel and Axle is easy to recognize. It consists of a wheel with a rod in the middle. You probably already know that it"s easier to move something heavy if you can put it in something with wheels, but you might not know why. For one thing, using wheels reduces the friction - or resistance between surfaces - between the load and the ground. Secondly, much like the lever, a smaller force applied to the rim of the wheel is converted to a larger force traveling a smaller distance at the axle. Wheel and axles are used for machines such as cars, bicycles, and scooters, but they are also used in other ways, like doorknobs and pencil sharpeners. A Pulley is a machine that uses a wheel with a rope wrapped around it. The wheel often has a groove in it, which the rope fits into. One end of the rope goes around the load, and the other end is where you apply the force. Pulleys can be used to move loads or change the direction of the force you are using, and help make work easier by allowing you to spread a weaker force out along a longer path to accomplish a job. By linking multiple pulleys together, you can do the same job with even less force, because you are applying the force along a much longer distance. Pulleys may be used to raise and lower flags, blinds, or sails, and are used to help raise and lower elevators. An Inclined Plane is a flat surface with one end higher than the other. Inclined planes allow loads to slide up to a higher level instead of being lifted, which allows the work to be accomplished with a smaller force spread over a longer distance. You may recognize an inclined plane as the simple machine used in ramps and slides. A Wedge is simply two inclined planes placed back to back. It is used to push two objects apart. A smaller force applied to the back of the wedge is converted to a greater force in a small area at the tip of the wedge. Examples of wedges are axes, knives, and chisels. A Screw is basically an inclined plane wrapped around a pole. Screws can be used to hold things together or to lift things. Just like the inclined plane, the longer the path the force takes, the less force is required to do the work. Screws with more threads take less force to do a job since the force has to travel a longer distance. Examples of screws are screws, nuts, bolts, jar lids, and lightbulbs. These six simple machines can be combined to form compound or complex machines, and are considered by some to be the foundation of all machinery. For example, a wheelbarrow is made of levers combined with a wheel and axle. A pair of scissors is another complex machine: the two blades are wedges, but they are connected by a lever that allows them to come together and cut. We use simple machines to help us do work every day. Every time you open a door or a bottle, cut up your food, or even just climb stairs, you are using simple machines. Take a look and see if you can identify the simple machines around you and figure out how they make it easier to do work.

  Contents

History

The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw . He discovered the principle of mechanical advantage in the lever. Archimedes" famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth." (Greek : δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ) expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to roughly calculate their mechanical advantage. For example, Heron of Alexandria (ca. 10–75 AD) in his work Mechanics lists five mechanisms that can "set a load in motion"; lever , windlass , pulley , wedge , and screw , and describes their fabrication and uses. However the Greeks" understanding was limited to the statics of simple machines; the balance of forces, and did not include dynamics ; the tradeoff between force and distance, or the concept of work .

Frictionless analysis

Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force F in {\displaystyle F_{\text{in}}\,} is applied to the device at one point, and it does work moving a load, F out {\displaystyle F_{\text{out}}\,} at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage

M A = F out / F in {\displaystyle \mathrm {MA} =F_{\text{out}}/F_{\text{in}}\,}

that can be calculated from the machine"s geometry and friction.

The mechanical advantage can be greater or less than one:

• The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
• In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
• A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.

A machine will be self-locking if and only if its efficiency η is below 50%:

η ≡ F o u t / F i n d i n / d o u t < 0.50 {\displaystyle \eta \equiv {\frac {F_{out}/F_{in}}{d_{in}/d_{out}}}<0.50\,}

Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio d in /d out (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.

Proof

When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work W 1,2 {\displaystyle W_{\text{1,2}}\,} is equal to the sum of the work done on the load force W load {\displaystyle W_{\text{load}}\,} and the work lost to friction

W 1,2 = W load + W fric (1) {\displaystyle W_{\text{1,2}}=W_{\text{load}}+W_{\text{fric}}\qquad \qquad (1)\,}

If the efficiency is below 50% η = W load / W 1,2 < 1 / 2 {\displaystyle \eta =W_{\text{load}}/W_{\text{1,2}}<1/2\,}

2 W load < W 1,2 {\displaystyle 2W_{\text{load}} 2 W load < W load + W fric {\displaystyle 2W_{\text{load}} W load < W fric {\displaystyle W_{\text{load}}

When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction W fric {\displaystyle W_{\text{fric}}\,} is the same

W load = W 2,1 + W fric {\displaystyle W_{\text{load}}=W_{\text{2,1}}+W_{\text{fric}}\,}

So the output work is

W 2,1 = W load − W fric < 0 {\displaystyle W_{\text{2,1}}=W_{\text{load}}-W_{\text{fric}}<0\,}

Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force

Modern machine theory

Kinematic chains

Classification of machines

The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines.

However, a more successful strategy was identified by Franz Reuleaux , who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.

This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint , sliding joint , cam joint and gear joint , and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints.

See also

References

1. Chambers, Ephraim (1728), "Table of Mechanicks", Cyclopædia, A Useful Dictionary of Arts and Sciences , London, England, Volume 2, p. 528, Plate 11 .
2. Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005), Mechanical sciences: engineering mechanics and strength of materials , Prentice Hall of India, p. 215, ISBN .
3. ^ Asimov, Isaac (1988), Understanding Physics , New York, New York, USA: Barnes & Noble, p. 88, ISBN .
4. Anderson, William Ballantyne (1914). Physics for Technical Students: Mechanics and Heat . New York, USA: McGraw Hill. pp. 112–122. Retrieved 2008-05-11 .
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6. ^ Usher, Abbott Payson (1988). A History of Mechanical Inventions . USA: Courier Dover Publications. p. 98. ISBN .
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8. ^ Prater, Edward L. (1994), Basic machines (PDF) , U.S. Navy Naval Education and Training Professional Development and Technology Center, NAVEDTRA 14037.
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12. ^ Chiu, Y. C. (2010), An introduction to the History of Project Management , Delft: Eburon Academic Publishers, p. 42,

(15 minutes)

• Distribute small toy cars that have wheels joined by axles to groups of students. Kick-start a discussion with some questions about the toy car mechanics, such as: How do these toy cars move? How are the wheels on each side of the car joined to each other?
• Have a student volunteer point to the rod that holds the two wheels together. Explain that the bar that joins two wheels is called an axle .
• Tell students that they will be learning about wheels and axles.
• Hold up the doorknob, explaining that it is an everyday example of a wheel and axle.
• Challenge the students to help you identify the wheel and axle in the doorknob. Listen as different students call out their guesses.
• After some speculation, tell students that the knob that turns is the wheel. The inner rod that is attached to the knob is the axle.
• Demonstrate how the wheel and axle works by turning the knob (wheel). That turns the inner rod (axle) and moves the latch, to open the door.

Guided Practice

(15 minutes)

• To consolidate student thinking, set up activity stations with play dough and a rolling pin.
• Let students practice flattening the dough with the pin.
• Guide them to express these understandings: The rolling pin is a wheel and axle. When you push on the handles (the axle) the wheel turns and flattens out the dough.
• Challenge students to think of other common machines that have one wheel like the rolling pin. Great examples include a wheelbarrow, a top, and a playground merry-go-round.

Independent working time

(15 minutes)

• Pass out a copy of the Wheel and Axle worksheet to each student to complete independently.
• Walk around the classroom to offer support to students who get stuck.

Differentiation

• Enrichment: Have students who need more of a challenge read a history of other simple machines, and fill out an accompanying word search.
• Support: Put students who need more support into pairs to complete the Wheel and Axle worksheet.

Assessment

(10 minutes)

• Collect the worksheets that the students have filled out, and correct them using the Wheel and Axle answer sheet.

Review and closing

(5 minutes)

• In summary, remind students that the rolling pin is a wheel and axle. When you push on the handles (the axle) the wheel turns and flattens out the dough.
• Challenge students to think of other common machines that have one wheel like the rolling pin, such as a wheelbarrow, top, and merry-go-round.
• Remind your class that the wheel and axle is only one of six common simple machines that help things move. For homework or additional independent work, consider encouraging students to learn more about other kinds of simple machines.

). The steeper the slope, or incline, the more nearly the required force approaches the actual weight. Expressed mathematically, the force F required to move a block D up an inclined plane without friction is equal to its weight W times the sine of the angle the inclined plane makes with the horizontal (θ). The equation is F = W sin θ.

In this representation of an inclined plane, D represents a block to be moved up the plane, F represents the force required to move the block, and W represents the weight of the block. Expressed mathematically, and assuming the plane to be without friction, F = W sin θ.

The principle of the inclined plane is used widely-for example, in ramps and switchback roads, where a small force acting for a distance along a slope can do a large amount of work.

The

A lever is a bar or board that rests on a support called a fulcrum. A downward force exerted on one end of the lever can be transferred and increased in an upward direction at the other end, allowing a small force to lift a heavy weight.

Two examples of levers(Left) A crowbar, supported and turning freely on a fulcrum f , multiplies a downward force F applied at point a such that it can overcome the load P exerted by the mass of the rock at point b . If, for example, the length a f is five times b f , the force F will be multiplied five times. (Right) A nutcracker is essentially two levers connected by a pin joint at a fulcrum f . If a f is three times b f , the force F exerted by hand at point a will be multiplied three times at b , easily overcoming the compressive strength P of the nutshell. Encyclopædia Britannica, Inc.

All early people used the lever in some form, for example, for moving heavy stones or as digging sticks for land cultivation. The principle of the lever was used in the swape, or , a long lever pivoted near one end with a platform or water container hanging from the short arm and counterweights attached to the long arm. A man could lift several times his own weight by pulling down on the long arm. This device is said to have been used in Egypt and India for raising water and lifting soldiers over battlements as early as 1500 bce .

Shadoof, central Anatolia, Turkey. Noumenon

The

A wedge is an object that tapers to a thin edge. Pushing the wedge in one direction creates a force in a sideways direction. It is usually made of metal or wood and is used for splitting, lifting, or tightening, as in securing a hammer head onto its handle.

The wedge was used in prehistoric times to split logs and rocks; an is also a wedge, as are the teeth on a saw. In terms of its mechanical function, the screw may be thought of as a wedge wrapped around a cylinder.

The

A wheel and axle is made up of a circular frame (the wheel) that revolves on a shaft or rod (the axle). In its earliest form it was probably used for raising weights or water buckets from wells.

Its principle of operation is best explained by way of a device with a large and a small gear attached to the same shaft. The tendency of a force, F , applied at the radius R on the large gear to turn the shaft is sufficient to overcome the larger force W at the radius r on the small gear. The force amplification, or , is equal to the ratio of the two forces (W :F ) and also equal to the ratio of the radii of the two gears (R :r ).

Two wheel and axle arrangements(A) With a large gear and a small gear attached to the same shaft, or axle, a force F applied at the radius R on the large gear is sufficient to overcome the larger force W at the radius r on the small gear, turning the axle. (B) In a drum and rope arrangement capable of raising weights, a large drum of radius R can be used to turn a small drum. An increase in mechanical advantage can be obtained by using the large drum to turn a small drum with two radii as well as a pulley block. When a force F is applied to the rope wrapped around the large drum, the rope wrapped around the small two-radius drum winds off of d (radius r 1) and onto D (radius r 2). The force W on the radius of the pulley block P is easily overcome, and the attached weight is lifted. Encyclopædia Britannica, Inc.

If the large and small gears are replaced with large- and small-diameter drums that are wrapped with ropes, the wheel and axle becomes capable of raising weights. The weight being lifted is attached to the rope on the small drum, and the operator pulls the rope on the large drum. In this arrangement the mechanical advantage is the radius of the large drum divided by the radius of the small drum. An increase in the mechanical advantage can be obtained by using a small drum with two radii, r 1 and r 2 , and a pulley block. When a force is applied to the large drum, the rope on the small drum winds onto D and off of d.

A measure of the force amplification available with the pulley-and-rope system is the velocity ratio, or the ratio of the at which the force is applied to the rope (V F ) to the velocity at which the weight is raised (V W ). This ratio is equal to twice the radius of the large drum divided by the difference in the radii of the smaller drums D and d. Expressed mathematically, the equation is V F /V W = 2R /(r 2 - r 1). The actual mechanical advantage W /F is less than this velocity ratio, depending on friction. A very large mechanical advantage may be obtained with this arrangement by making the two smaller drums D and d of nearly equal radius.

The

A pulley is a wheel that carries a flexible rope, cord, cable, chain, or belt on its rim. Pulleys are used singly or in combination to transmit and motion. Pulleys with grooved rims are called sheaves. In , pulleys are affixed to shafts at their axes, and power is transmitted between the shafts by means of endless belts running over the pulleys.

GK Bloemsma

One or more independently rotating pulleys can be used to gain mechanical advantage, especially for lifting weights. The shafts about which the pulleys turn may affix them to frames or blocks, and a combination of pulleys, blocks, and rope or other flexible material is referred to as a . The Greek mathematician (3rd century bce ) is reported to have used compound pulleys to pull a ship onto dry land.

Encyclopædia Britannica, Inc.

The

A screw is a usually circular cylindrical member with a continuous helical rib, used either as a fastener or as a force and motion modifier.

Although the Pythagorean philosopher (5th century bce ) is the alleged inventor of the screw, the exact period of its first appearance as a useful mechanical device is obscure. The invention of the is usually ascribed to Archimedes, but evidence exists of a similar device used for irrigation in Egypt at an earlier date. The screw press, probably invented in Greece in the 1st or 2nd century bce , has been used since the days of the Roman Empire for pressing clothes. In the 1st century ce , wooden screws were used in wine and olive-oil presses, and cutters (taps) for cutting internal threads were in use.

Screws and screw heads (A) Cap screw, (B) machine screw with oval head, (C) setscrew with hollow head, (D) self-tapping screw, (E) flat-head wood screw, (F) machine screw with Phillips head, (G) lag screw Encyclopædia Britannica, Inc.

Are made in a wide variety of diameters and lengths; when using the larger sizes, pilot holes are drilled to avoid splitting the wood. are large wood screws used to fasten heavy objects to wood. Heads are either square or hexagonal.

Screws that modify force and motion are known as . A screw jack converts (turning moment) to thrust. The thrust (usually to lift a heavy object) is created by turning the screw in a stationary nut. By using a long bar to turn the screw, a small force at the end of the bar can create a large thrust force. Workpiece tables on are moved linearly on guiding ways by screws that rotate in at the ends of the tables and mate with nuts fixed to the machine frame. A similar torque-to-thrust conversion can be obtained by either rotating an axially fixed screw to drive a rotationally fixed nut along the screw or by rotating an axially fixed nut to drive a rotationally fixed screw through the nut.

This article was most recently revised and updated by Robert Curley , Senior Editor.