the assignment of work to specific machines

Quiz 16: Aggregate Planning and Master Scheduling

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Aggregate planners typically use mathematical techniques such as linear programming for planning.

Aggregate planners commonly use trial-and-error methods in developing aggregate plans.

An advantage of a "chase" strategy for aggregate planning is that inventories can be kept relatively low.

Linear programming models yield the optimal solution.

The goal of aggregate planning is to achieve a production plan that effectively utilizes the organization's resources to meet expected demand.

The output from aggregate planning is a detailed business plan covering the next 2 to 12 months.

Seasonality in demand has the advantage of leveling out requirements for our product or service.

Aggregate planning is capacity planning that typically covers a time horizon of one to three months.

Organizations facing seasonal changes in demand are prevented from using aggregate planning techniques.

A level capacity strategy is also known as a chase demand strategy.

Capacity can be modified in aggregate planning by promotion and producing additional product using overtime.

The use of tables and charts in aggregate planning usually enables planners to arrive at an optimal plan.

Departmental budgeting is an example of aggregate planning.

Aggregate planners are concerned with the quality and quantity of expected demand.

Disaggregating an aggregate plan leads to a master schedule.

Ultimately the overriding factor in choosing a strategy in aggregate planning is overall cost.

Aggregate planning is used to establish general levels of employment, output, and inventories over an intermediate range of time.

The master schedule indicates the quantity and timing for delivery of a product, but not the dates production will need to start.

The assignment of work to specific machines and people are examples of aggregate planning.

Demand can be altered in aggregate planning by promotion and producing additional product using overtime.

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Assignment Method: Examples of How Resources Are Allocated

What Is the Assignment Method?

The assignment method is a way of allocating organizational resources in which each resource is assigned to a particular task. The resource could be monetary, personnel , or technological.

Understanding the Assignment Method

The assignment method is used to determine what resources are assigned to which department, machine, or center of operation in the production process. The goal is to assign resources in such a way to enhance production efficiency, control costs, and maximize profits.

The assignment method has various applications in maximizing resources, including:

• Allocating the proper number of employees to a machine or task
• Allocating a machine or a manufacturing plant and the number of jobs that a given machine or factory can produce
• Assigning a number of salespersons to a given territory or territories
• Assigning new computers, laptops, and other expensive high-tech devices to the areas that need them the most while lower priority departments would get the older models

Companies can make budgeting decisions using the assignment method since it can help determine the amount of capital or money needed for each area of the company. Allocating money or resources can be done by analyzing the past performance of an employee, project, or department to determine the most efficient approach.

Regardless of the resource being allocated or the task to be accomplished, the goal is to assign resources to maximize the profit produced by the task or project.

Example of Assignment Method

A bank is allocating its sales force to grow its mortgage lending business. The bank has over 50 branches in New York but only ten in Chicago. Each branch has a staff that is used to bring in new clients.

The bank's management team decides to perform an analysis using the assignment method to determine where their newly-hired salespeople should be allocated. Given the past performance results in the Chicago area, the bank has produced fewer new clients than in New York. The fewer new clients are the result of having a small market presence in Chicago.

As a result, the management decides to allocate the new hires to the New York region, where it has a greater market share to maximize new client growth and, ultimately, revenue.

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• TeachEngineering
• Engineering: Simple Machines

Lesson Engineering: Simple Machines

Grade Level: 4 (3-5)

Time Required: 30 minutes

Lesson Dependency: None

Subject Areas: Geometry, Physical Science, Problem Solving, Reasoning and Proof, Science and Technology

• Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

• Stack It Up!
• Choosing a Pyramid Site
• Solid Rock to Building Block
• Wheeling It In!
• Watch It Slide!
• Pulley'ing Your Own Weight
• Modern Day Pyramids

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Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, introduction/motivation, associated activities, lesson closure, vocabulary/definitions, additional multimedia support, user comments & tips.

Why do engineers care about simple machines? How do such devices help engineers improve society? Simple machines are important and common in our world today in the form of everyday devices (crowbars, wheelbarrows, highway ramps, etc.) that individuals, and especially engineers, use on a daily basis. The same physical principles and mechanical advantages of simple machines used by ancient engineers to build pyramids are employed by today's engineers to construct modern structures such as houses, bridges and skyscrapers. Simple machines give engineers added tools for solving everyday challenges.

After this lesson, students should be able to:

• Understand what a simple machine is and how it would help an engineer to build something.
• Identify six types of simple machines.
• Understand how the same physical principles used by engineers today to build skyscrapers were employed in ancient times by engineers to build pyramids.
• Generate and compare multiple possible solutions to creating a simple lever machine based on how well each met the constraints of the challenge.

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How did the Egyptians build the Great Pyramids thousands of years ago (~2,500 BCE)? Could you build a pyramid using 9,000-kilogram (~10-ton or 20,000-lb) blocks of stone with your bare hands? That's like trying to move a large elephant with your bare hands! How many people might it take to move a block that big? It would still be a challenge to build a pyramid today even with modern tools, such as jackhammers, cranes, trucks and bulldozers. But without these modern tools, how did Egyptian workers cut, shape, transport and place enormous stones? Well, one key to accomplishing this amazing and difficult task was the use of simple machines.

Simple machines are devices with no, or very few, moving parts that make work easier. Many of today's complex tools are really just more complicated forms of the six simple machines. By using simple machines, ordinary people can split huge rocks, hoist large stones, and move blocks over great distances.

However, it took more than just simple machines to build the pyramids. It also took tremendous planning and a great design . Planning, designing, working as a team and using tools to create something, or to get a job done, is what engineering is all about. Engineers use their knowledge, creativity and problem-solving skills to accomplish some amazing feats to solve real-world challenges. People call on engineers to use their understanding of how things work to do seemingly impossible jobs and make everyday activities easier. It is surprising how many times engineers turn to simple machines to solve these problems.

Once we understand simple machines, you will recognize them in many common activities and everyday items. (Hand out Simple Machines Reference Sheet .) These are the six simple machines: wedge, wheel and axle, lever, inclined plane, screw , and pulley . Now that you see the pictures, do you recognize some of these simple machines? Can you see any of these simple machines around the classroom? How do they work? Well, an important vocabulary term when learning about simple machines is the phenomenon of  mechanical advantage . Mechanical advantage of simple machines means we can use less force to move an object, but we have to move it a longer distance. A good example is pushing a heavy object up a ramp. It may be easier to push the object up a ramp instead of just lifting it up to the right height, but it takes a longer distance. A ramp is an example of the simple machine called an inclined plane . We are going to learn a lot more about each of these six simple machines that are a simple solution to helping engineers, and all humans, do hard work.

Sometimes it is difficult to recognize simple machines in our lives because they look different than the examples we see at school. To make our study of simple machines easier, let's imagine that we are living in ancient Egypt and that the leader of the country has hired us as engineers to build a pyramid. Students can act as engineers with the fun and hands-on activities: Stack It Up! and Choosing a Pyramid Site to design and plan the construction of a new pyramid. Today's availability of electricity and technologically-advanced machines make it difficult for us to see what the simple machine is accomplishing. But in the context of ancient Egypt, the simple machines that we will study are the much more basic tools of the time. After we develop an understanding of simple machines, we will shift our context to building a skyscraper in the present day, so we can compare and contrast how simple machines were used across the centuries and are still used today.

Lesson Background and Concepts for Teachers

Use the attached Introduction to Simple Machines PowerPoint presentation and Simple Machines Reference Sheet as helpful classroom tools. (Show the PowerPoint presentation, or print out the slides to use with an overhead projector. The presentation is animated to promote an inquiry-based style; each click reveals a new point about each machine; have students suggest characteristics and examples before you reveal them.)

Simple machines are everywhere; we use them everyday to perform simple tasks. Simple machines have also been in use since the early days of human existence. While simple machines take many shapes, they come in six basic types:

• Wedge : A device that forces things apart.
• Wheel and axle : Used to reduce friction.
• Lever : Moves around a pivot point to increase or decrease mechanical advantage.
• Inclined plane : Raises objects by moving up a slope.
• Screw : A device that can lift or hold things together.
• Pulley : Changes the direction of a force.

Simple Machines

We use simple machines because they make work easier. The scientific definition of work is the amount of force that is applied to an object multiplied by the distance the object is moved. Thus, work consists of force and distance. Each job takes a specific amount of work to finish it, and this number does not change. Thus, the force times the distance always equals the same amount of work. This means that if you move something a smaller distance you need to exert a greater force. On the other hand, if you want to exert less force, you need to move it over a greater distance. This is the force and distance trade off, or mechanical advantage , which is common to all simple machines. With mechanical advantage, the longer a job takes, the less force you need to use throughout the job. Most of the time, we feel that a task is hard because it requires us to use a lot of force. Therefore, using the trade off between distance and force can make our task much easier to complete.

The wedge is a simple machine that forces objects or substances apart by applying force to a large surface area on the wedge, with that force magnified to a smaller area on the wedge to do the actual work. A nail is a common wedge with a wide nail head area where the force is applied, and a small point area where the concentrated force is exerted. The force is magnified at the point, enabling the nail to pierce wood. As the nail sinks into the wood, the wedge shape at the point of the nail moves forward, and forces the wood apart.

Everyday examples of wedges include an axe (see Figure 1), nail, doorstop, chisel, saw, jackhammer, zipper, bulldozer, snow plow, horse plow, zipper, airplane wing, knife, fork and bow of a boat or ship.

Wheel and Axle

The wheel and axle is a simple machine that reduces the friction involved in moving an object, making the object easier to transport. When an object is pushed, the force of friction must be overcome to start it moving. Once the object is moving, the force of friction opposes the force exerted on the object. The wheel and axle makes this easier by reducing the friction involved in moving an object. The wheel rotates around an axle (essentially a rod that goes through the wheel, letting the wheel turn), rolling over the surface and minimizing friction. Imagine trying to push a 9,000-kilogram (~10-ton) block of stone. Wouldn't it be easier to roll it along using logs placed underneath the stone?

Everyday examples of the wheel and axle include a car, bicycle, office chair, wheel barrow, shopping cart, hand truck and roller skates.

A lever simple machine consists of a load, a fulcrum and effort (or force). The load is the object that is moved or lifted. The fulcrum is the pivot point, and the effort is the force required to lift or move the load. By exerting a force on one end of the lever (the applied force), a force at the other end of the lever is created. The applied force is either increased or decreased, depending on the distance from the fulcrum (the point or support on which a lever pivots) to the load, and from the fulcrum to the effort.

Everyday examples of levers include a teeter-totter or see-saw, crane arm, crow bar, hammer (using the claw end), fishing pole and bottle opener. Think of a how you use a crowbar (see Figure 2). By pushing down on the long end of the crowbar, a force is created at the load end over a smaller distance, once again, demonstrating the tradeoff between force and distance.

Inclined Plane

Inclined planes make it easier to lift something. Think of a ramp. Engineers use ramps to easily move objects to a greater height. There are two ways to raise an object: by lifting it straight up, or by pushing it diagonally up. Lifting an object straight up moves it over the shortest distance, but you must exert a greater force. On the other hand, using an inclined plane requires a smaller force, but you must exert it over a longer distance.

Everyday examples of inclined planes include highway access ramps, sidewalk ramps, stairs, inclined conveyor belts, and switchback roads or trails.

A screw is essentially an inclined plane wrapped around a shaft. Screws have two primary functions: they hold things together, or they lift objects. A screw is good for holding things together because of the threading around the shaft. The threads grip the surrounding material like teeth, resulting in a secure hold; the only way to remove a screw is to unwind it. A car jack is an example of a screw being used to lift something (see Figure 3).

Everyday examples of screws include a screw, bolt, clamp, jar lid, car jack, spinning stool and spiral staircase.

A pulley is a simple machine used to change the direction of a force. Think of raising a flag or lifting a heavy stone. To lift a stone up into its place on a pyramid, one would have to exert a force that pulls it up. By using a pulley made from a grooved wheel and rope, one can pull down on the rope, capitalizing on the force of gravity, to lift the stone up . Even more valuable, a system of several pulleys can be used together to reduce the force needed to lift an object.

Everyday examples of pulleys in use include flag poles, elevators, sails, fishing nets (see Figure 4), clothes lines, cranes, window shades and blinds, and rock climbing gear.

Compound Machines

A compound machine is a device that combines two or more simple machines. For example, a wheelbarrow combines the use of a wheel and axle with a lever. Using the six basic simple machines, all sorts of compound machines can be made. There are many simple and compound machines in your home and classroom. Some examples of the compound machines you may find are a can opener (wedge and lever), exercise machines/cranes/tow trucks (levers and pulleys), shovel (lever and wedge), car jack (lever and screw), wheel barrow (wheel and axle and lever) and bicycle (wheel and axle and pulley).

Watch this activity on YouTube

• Choosing a Pyramid Site - Working in engineering project teams, students choose a site for the construction of a pyramid. They base their decision on site features as provided by a surveyor's report; distance from the quarry, river and palace; and other factors they deem important to the project.

Today, we have discussed six simple machines. Who can name them for me? (Answer: Wedge, wheel and axle, lever, inclined plane, screw, and pulley.) How do simple machines make work easier? (Answer: Mechanical advantage enables us to use less force to move an object, but we have to move it a longer distance.) Why do engineers use simple machines? (Possible answers: Engineers creatively use their knowledge of science and math to make our lives better, often using simple machines. They invent tools that make work easier. They accomplish huge tasks that could not be done without the mechanical advantage of simple machines. They design structures and tools to use our environmental resources better and more efficiently.) Tonight, at home, think about everyday examples of the six simple machines. See how many you can find around your house!

Complete the KWL Assessment Chart (see the Assessment section). Gauge students' understanding of the lesson by assigning the Simple Machines Worksheet as a take-home quiz. As an extension, use the attached Simple Machines Scavenger Hunt! Worksheet to conduct a simple machines scavenger hunt in which students find examples of simple machines used in the classroom and at home.

In other lessons of this unit, students study each simple machine in more detail and see how each could be used as a tool to build a pyramid or a modern building.

design: (verb) To plan out in systematic, often graphic form. To create for a particular purpose or effect. Design a building. (noun) A well thought-out plan.

Engineering: Applying scientific and mathematical principles to practical ends such as the design, manufacture and operation of efficient and economical structures, machines, processes and systems.

force: A push or pull on an object.

inclined plane: A simple machine that raises an object to greater height. Usually a straight slanted surface and no moving parts, such as a ramp, sloping road or stairs.

lever: A simple machine that increases or decreases the force to lift something. Usually a bar pivoted on a fixed point (fulcrum) to which force is applied to do work.

mechanical advantage : An advantage gained by using simple machines to accomplish work with less effort. Making the task easier (which means it requires less force), but may require more time or room to work (more distance, rope, etc.). For example, applying a smaller force over a longer distance to achieve the same effect as applying a large force over a small distance. The ratio of the output force exerted by a machine to the input force applied to it.

pulley: A simple machine that changes the direction of a force, often to lift a load. Usually consists of a grooved wheel in which a pulled rope or chain runs.

pyramid: A massive structure of ancient Egypt and Mesoamerica used for a crypt or tomb. The typical shape is a square or rectangular base at the ground with sides (faces) in the form of four triangles that meet in a point at the top. Mesoamerican temples have stepped sides and a flat top surmounted by chambers.

screw: A simple machine that lifts or holds materials together. Often a cylindrical rod incised with a spiral thread.

simple machine: A machine with few or no moving parts that is used to make work easier (provides a mechanical advantage). For example, a wedge, wheel and axle, lever, inclined plane, screw, or pulley.

spiral: A curve that winds around a fixed center point (or axis) at a continuously increasing or decreasing distance from that point.

tool: A device used to do work.

wedge: A simple machine that forces materials apart. Used for splitting, tightening, securing or levering. It is thick at one end and tapered to a thin edge at the other.

wheel and axle: A simple machine that reduces the friction of moving by rolling. A wheel is a disk designed to turn around an axle passed through the center of the wheel. An axle is a supporting cylinder on which a wheel or a set of wheels revolves.

work: Force on an object multiplied by the distance it moves. W = F x d (force multiplied by distance).

Pre-Lesson Assessment

Know / Want to Know / Learn (KWL) Chart: Create a classroom KWL chart to help organize learning about a new topic. On a large sheet of paper or on the classroom board, draw a chart with the title "Building with Simple Machines." Draw three columns titled, K, W and L, representing what students know about simple machines, what they want to know about simple machines and what they learned about simple machines. Fill out the K and W sections during the lesson introduction as facts and questions emerge. Fill out the L section at the end of the lesson.

Post-Introduction Assessment

Reference Sheet: Hand out the attached Simple Machines Reference Sheet . Review the information and answer any questions. Suggest the students keep the sheet handy in their desks, folders or journals.

Observations: Show students an example of each simple machine and have them make observations and discuss any patterns that can be used to predict future motion. 

Lesson Summary Assessment

Closing Discussion: Conduct an informal class discussion, asking the students what they learned from the activities. Ask the students:

• Who can name the different types of simple machines? (Answer: Wedge, wheel and axle, lever, inclined plane, screw, and pulley.)
• How do simple machines make work easier? (Answer: Mechanical advantage enables us to use less force to move an object, but we have to move it a longer distance.)
• Why do engineers use simple machines? (Possible answers: Engineers creatively use their knowledge of science and math to make our lives better, often using simple machines. They invent tools that make work easier. They accomplish huge tasks that could not be done without the mechanical advantage of simple machines. They design structures and tools to use our environmental resources better and more efficiently.)

Remind students that engineers consider many factors when they plan, design and create something. Ask the students:

• What are the considerations an engineer must keep in mind when designing a new structure? (Possible answers: Size and shape (design) of the structure, available construction materials, calculation of materials needed, comparing materials and costs, making drawings, etc.)
• What are the considerations an engineer must keep in mind when choosing a site to build a new structure? (Possible answers: Site physical characteristics [topography, soil foundation], distance to construction resources [wood, stone, water, concrete], suitability for the structure's purpose [locate a school or grocery store near where people live].)

KWL Chart (Conclusion): As a class, finish column L of the KWL Chart as described in the Pre-Lesson Assessment section. List all of the things they learned about simple machines. Were all of the W questions answered? What new things did they learn?

Take-Home Quiz: Gauge students' understanding of the lesson by assigning the Simple Machines Worksheet as a take-home quiz.

Lesson Extension Activities

Use the attached Simple Machines Scavenger Hunt! Worksheet to conduct a fun scavenger hunt. Have the students find examples of all the simple machines used in the classroom and their homes.

Bring in everyday examples of simple machines and demonstrate how they work.

Illustrate the power of simple machines by asking students to do a task without using a simple machine, and then with one. For example, create a lever demonstration by hammering a nail into a piece of wood. Have students try to pull the nail out, first using only their hands

Bring in a variety of everyday examples of simple machines. Hand out one out to each student and have them think about what type of simple machine it is. Next, have students place the items into categories by simple machines and explain why they chose to place their item there. Ask students what life would be like without this item. Emphasize that simple machines make our life easier.

See the Edheads website for an interactive game on simple machines: http://edheads.org.

Engineering Design Fun with Levers: Give each pair of students a paint stirrer, 3 small plastic cups, a piece of duct tape and a wooden block or spool (or anything similar). Challenge the students to design a simple machine lever that will throw a ping pong ball (or any other type of small ball) as high as possible. In the re-design phase, allow the students to request materials to add on to their design. Have a small competition to see which group was able to send the ping pong ball flying high. Discuss with the class why that particular design was successful versus other variations seen during the competition.

See http://edheads.org for a good simple machines website with curricular materials including educational games and activities.

Students are introduced to three of the six simple machines used by many engineers: lever, pulley, and wheel-and-axle. In general, engineers use the lever to magnify the force applied to an object, the pulley to lift heavy loads over a vertical path, and the wheel-and-axle to magnify the torque appl...

Students explore building a pyramid, learning about the simple machine called an inclined plane. They also learn about another simple machine, the screw, and how it is used as a lifting or fastening device.

Students learn how simple machines, including wedges, were used in building both ancient pyramids and present-day skyscrapers. In a hands-on activity, students test a variety of wedges on different materials (wax, soap, clay, foam).

Refreshed with an understanding of the six simple machines; screw, wedge, pully, incline plane, wheel and axle, and lever, student groups receive materials and an allotted amount of time to act as mechanical engineers to design and create machines that can complete specified tasks.

Dictionary.com. Lexico Publishing Group, LLC. Accessed January 11, 2006. (Source of some vocabulary definitions, with some adaptation) http://www.dictionary.com

Simple Machines. inQuiry Almanack, The Franklin Institute Online, Unisys and Drexel eLearning. Accessed January 11, 2006. http://sln.fi.edu/qa97/spotlight3/spotlight3.html

Contributors

Supporting program, acknowledgements.

The contents of these digital library curricula were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government. 

Last modified: August 16, 2024

6 simple machines: Making work easier

The simple machines that changed the world throughout history.

Wheel and axle

Inclined plane, additional resources, bibliography.

Throughout history, humans have developed several simple machines to make work easier. The most notable of these are known as the "six simple machines": the wheel and axle, the lever, the inclined plane, the pulley, the screw, and the wedge, although the latter three are actually just extensions or combinations of the first three, according to Encyclopedia Britannica .

Because work is defined as force acting on an object in the direction of motion, a machine makes work easier to perform by accomplishing one or more of the following functions, according to Boston University :

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

Simple machines are devices with no, or very few, moving parts that make work easier. Many of today's complex tools are just combinations or more complicated forms of the six simple machines, according to the University of Colorado at Boulder . For instance, we might attach a long handle to a shaft to make a windlass, or use a block and tackle to pull a load up a ramp. While these machines may seem simple, they continue to provide us with the means to do many things that we could never do without them.

The wheel is considered to be one of the most significant inventions in the history of the world. "Before the invention of the wheel in 3500 B.C., humans were severely limited in how much stuff we could transport over land, and how far," as Live Science has previously reported . Wheeled carts facilitated agriculture and commerce by enabling the transportation of goods to and from markets, as well as easing the burdens of people traveling great distances, 

The wheel greatly reduces the friction encountered when an object is moved over a surface. "If you put your file cabinet on a small cart with wheels, you can greatly reduce the force you need to apply to move the cabinet with constant speed," according to the University of Tennessee.

In his book " Ancient Science: Prehistory-A.D. 500 " , Charlie Samuels writes, "In parts of the world, heavy objects such as rocks and boats were moved using log rollers. As the object moved forward, rollers were taken from behind and replaced in front." This was the first step in the development of the wheel.

The great innovation, though, was in mounting a wheel on an axle. The wheel could be attached to an axle that was supported by a bearing, or it could be made to turn freely about the axle. This led to the development of carts, wagons and chariots. According to Samuels, archaeologists use the development of a wheel that rotates on an axle as an indicator of a relatively advanced civilization. The earliest evidence of wheels on axles is from about 3200 B.C. by the Sumerians. The Chinese independently invented the wheel in 2800 B.C.

– Perpetual motion machines: Working against physical laws

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– Who invented the steam engine?

– History of computers: A brief timeline

In addition to reducing friction, a wheel and axle can also serve as a force multiplier. If a wheel is attached to an axle, and a force is used to turn the wheel, the rotational force, or torque, on the axle is much greater than the force applied to the rim of the wheel. Alternatively, a long handle can be attached to the axle to achieve a similar effect.

The other five machines all help humans increase and/or redirect the force applied to an object. In their book " Moving Big Things , " Janet L. Kolodner and her co-authors write, "Machines provide mechanical advantage to assist in moving objects. Mechanical advantage is the trade-off between force and distance." In the following discussion of the simple machines that increase the force applied to their input, we will neglect the force of friction, because in most of these cases, the frictional force is very small compared to the input and output forces involved.

When a force is applied over a distance, it produces work. Mathematically , this is expressed as W = F × D. For example, to lift an object, we must do work to overcome the force due to gravity and move the object upward. To lift an object that is twice as heavy, it takes twice as much work to lift it the same distance. It also takes twice as much work to lift the same object twice as far, according to Auburn University . As indicated by the math , the main benefit of machines is that they allow us to do the same amount of work by applying a smaller amount of force over a greater distance.

"Give me a lever and a place to stand, and I'll move the world." This boastful claim is attributed to the third-century Greek philosopher, mathematician and inventor Archimedes . While it may be a bit of an exaggeration, it does express the power of leverage, which, at least figuratively, moves the world.

The genius of Archimedes was to realize that in order to accomplish the same amount or work, one could make a trade-off between force and distance using a lever. His Law of the Lever states, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights," according to " Archimedes in the 21st Century ," a virtual book by Chris Rorres at New York University.

The lever consists of a long beam and a fulcrum, or pivot. The mechanical advantage of the lever depends on the ratio of the lengths of the beam on either side of the fulcrum.

For example, say we want to lift a 100-lb. (45 kilograms) weight 2 feet (61 centimeters) off the ground. We can exert 100 lbs. of force on the weight in the upward direction for a distance of 2 feet , and we have done 200 pound-feet (271 Newton-meters) of work. However, if we were to use a 30-foot (9 m) lever with one end under the weight and a 1-foot (30.5 cm) fulcrum placed under the beam 10 feet (3 m) from the weight, we would only have to push down on the other end with 50 lbs. (23 kg) of force to lift the weight. However, we would have to push the end of the lever down 4 feet (1.2 m) in order to lift the weight 2 feet. We have made a trade-off in which we doubled the distance we had to move the lever, but we decreased the needed force by half in order to do the same amount of work.

The inclined plane is simply a flat surface raised at an angle, like a ramp. According to Bob Williams, a professor in the department of mechanical engineering at the Russ College of Engineering and Technology at Ohio University, an inclined plane is a way of lifting a load that would be too heavy to lift straight up. The angle (the steepness of the inclined plane) determines how much effort is needed to raise the weight. The steeper the ramp, the more effort is required. That means that if we lift our 100-lb. weight 2 feet by rolling it up a 4-foot ramp, we reduce the needed force by half while doubling the distance it must be moved. If we were to use an 8-foot (2.4 m) ramp, we could reduce the needed force to only 25 lbs. (11.3 kg).

If we want to lift that same 100-lb. weight with a rope, we could attach a pulley to a beam above the weight. This would let us pull down instead of up on the rope, but it still requires 100 lbs. of force. However, if we were to use two pulleys — one attached to the overhead beam, and the other attached to the weight — and we were to attach one end of the rope to the beam, run it through the pulley on the weight and then through the pulley on the beam, we would only have to pull on the rope with 50 lbs. of force to lift the weight, although we would have to pull the rope 4 feet to lift the weight 2 feet. Again, we have traded increased distance for decreased force.

If we want to use even less force over an even greater distance, we can use a block and tackle. According to course materials from the University of South Carolina, "A block and tackle is a combination of pulleys which reduces the amount of force required to lift something. The trade-off is that a longer length of rope is required for a block and tackle to move something the same distance."

As simple as pulleys are, they are still finding use in the most advanced new machines. For example, the Hangprinter, a 3D printer that can build furniture-sized objects, employs a system of wires and computer-controlled pulleys anchored to the walls, floor, and ceiling.

"A screw is essentially a long incline plane wrapped around a shaft, so its mechanical advantage can be approached in the same way as the incline," according to Georgia State University . Many devices use screws to exert a force that is much greater than the force used to turn the screw. These devices include bench vices and lug nuts on automobile wheels. They gain a mechanical advantage not only from the screw itself but also, in many cases, from the leverage of a long handle used to turn the screw.

According to the New Mexico Institute of Mining and Technology , "Wedges are moving inclined planes that are driven under loads to lift, or into a load to split or separate." A longer, thinner wedge gives more mechanical advantage than a shorter, wider wedge, but a wedge does something else: The main function of a wedge is to change the direction of the input force. For example, if we want to split a log, we can drive a wedge downward into the end of the log with great force using a sledgehammer, and the wedge will redirect this force outward, causing the wood to split. Another example is a doorstop, where the force used to push it under the edge of the door is transferred downward, resulting in frictional force that resists sliding across the floor.

John H. Lienhard, professor emeritus of mechanical engineering and history at the University of Houston, takes " another look at the invention of the wheel ." Check out the Center of Science and Industry in Columbus, Ohio, who has an interactive explanation of simple machines. HyperPhysics – a website produced by Georgia State University – also has illustrated explanations of the six simple machines.

Illinois State University, “ Resource Information for Teaching Simple Machines ”, January 2022. 

Victoria State Government, “ Simple Machines ”, March 2019. 

Canada Science and Technology Museum, “ Educational Programs: Simple Machines ”, January 2022. 

Yi Zhang et al, “ Introduction to Mechanisms ”, Carnegie Mellon University, January 2022.

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Simple Machines and How They Work

Simple machines are tools with few or no moving parts that change the magnitude or direction of a force . Basically, they multiply force and make work easier. Here is a look at the types of simple machines, how they work, and their uses.

What Is a Simple Machine?

A machine is a device that performs work by applying a force over a distance. Simple machines do work against a single load force in a way that increases the output force by decreasing the distance the load moves. The ratio of the output force to the applied force is called the mechanical advantage of the machine.

How Simple Machines Work

Basically, a simple machine relies on one or more of the following strategies:

• It changes the direction of a force.
• It increases the magnitude of a force.
• The machine transfers a force from one location to another.
• It increases the speed or distance of a force.

6 Simple Machines

There are six simple machines: the wheel and axle, lever, inclined plane, pulley, screw, and wedge.

Wheel and Axle

The wheel and axle makes transporting heavy goods easier and helps people travel distances. A wheel has a small footprint, so it reduces friction when you move an object over a surface. For example, there is a lot more friction in sliding a refrigerator across the floor than in wheeling it in a cart. A wheel and axle is also a force multiplier. The input force turns the wheel, generating a rotational force or torque, but the torque is much greater on the axle than on the rim of the wheel. A long handle attached to an axle achieves a comparable effect.

A lever makes a trade-off between force and distance. A see-saw is a familiar example of this type of simple machine. A lever has a long beam and a pivot or fulcrum. Depending on the placement of the fulcrum, you either use a lever for lifting a heavy load over a smaller distance than the input force or a lighter load over a larger distance than the input force.

Inclined Plane

An inclined plane is a ramp or angled flat surface. It increases the distance of a force. An inclined plane helps with lifting loads that are too heavy to lift straight up. But, the steeper the ramp, the more effort you need. For example, climbing a ramp is much easier than jumping a great height. Climbing a steep ramp takes a lot more effort than walking up a gentle slope.

A pulley either changes the direction of a force or else trades increased force for decreased distance. For example, it takes a lot of force to pull a bucket of water straight up from a well. Attaching a pulley lets your pull down on the rope instead of up, but it takes the same force. However, if you use two pulleys, with one attached to the bucket and the other attached to an overhead beam, you only apply half the force to pull up the bucket. The trade-off is that you double the distance of rope you pull. A block and tackle is a combination of pulleys that reduces the necessary force even more.

A screw is essentially an inclined plane, except it is wrapped around a shaft. The incline makes it easier to exert a greater force for turning the screw. Using a long handle, such as a screwdriver, increases the mechanical advantage. Screws find use in daily life as lug nuts on car wheels and for holding parts together in machines and furniture.

A wedge is a moving inclined plane that works by changing the direction of the input force. Common uses of wedges are for splitting pieces and lifting loads. For example, an axe is a wedge. So is a doorstop. The axe directs the force of a blow outward, splitting a log into pieces. A doorstop transfers the force of a moving door downward, producing friction that keeps it from sliding over the floor.

Ideal Simple Machines

An ideal simple machine is one that does not lose energy through friction, deformation, or wear. In such a situation, the power you put into the machine equals its power output.

P out = P in

In an ideal simple machine, the mechanical advantage is the ratio of force out to force in:

MA = F out / F in

Power equals the velocity multiplied by force:

F out ν out = F in ν in

It follows that the mechanical advantage of an ideal machine is its velocity ratio:

MA ideal = F out / F in = ν in / ν out

The velocity ration also equals the ratio of distance covered over time:

MA ideal = d in /d out

Note that ideal simple machines obey the law of conservation of energy . In other words, they cannot do more work than they get from the input force.

• If MA > 1 then the output force is greater than the input force, but the load moves a smaller distance than the distance moved by the input force.
• If MA < 1 then the output force is less than the input force and the load moves a greater distance than the distance moved by the input force.

Friction and Efficiency

In real life, machines have friction. Some of the input power gets lost as heat. Energy is conserved, so input power equals the sum of output power and friction:

P in = P out + P friction

Mechanical efficiency η is the ratio of power out to power in. It is a measure of friction energy loss and ranges from 0 (all power lost to friction) to 1 (an ideal simple machine):

η = P out / P in

Since power equals the product of force and velocity, the mechanical advantage of a real simple machine is:

MA = F out / F in = η (ν in / ν out )

In a non-ideal machine, mechanical advantage is always less than the velocity ratio. What this means it that a machine with friction never moves as large a load as its corresponding ideal machine.

People used simple machines since ancient time, without understanding how they work. The Mesopotamians likely invented the wheel between 4200 to 4000 BC. Historians credit the Greek philosopher Archimedes with the description of simple machines. In the 3rd century BC, Archimedes described the concept of mechanical advantage in the lever. He studied the screw and pulley, as well. Greek philosophers calculated the mechanical advantage of five of the six simple machines (not the inclined plane). In the 16th century, Leonardo da Vinci described the rules of sliding friction, although he did not publish this work. Guillaume Amontons rediscovered the rules of friction in 1699.

• Asimov, Isaac (1988). Understanding Physics . New York: Barnes & Noble. ISBN 978-0-88029-251-1.
• Morris, Christopher G. (1992). Academic Press Dictionary of Science and Technology . Gulf Professional Publishing. ISBN 9780122004001.
• Ostdiek, Vern; Bord, Donald (2005). Inquiry Into Physics . Thompson Brooks/Cole. ISBN 978-0-534-49168-0.
• Paul, Akshoy; Roy, Pijush; Mukherjee, Sanchayan (2005). Mechanical Sciences: Engineering Mechanics and Strength of Materials . Prentice Hall of India. ISBN 978-81-203-2611-8.
• Usher, Abbott Payson (1988). A History of Mechanical Inventions . US: Courier Dover Publications. ISBN 978-0-486-25593-4.

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The Long Run

A Vice Presidential Learning Curve: How Kamala Harris Picked Her Shots

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Credit... Erin Schaff/The New York Times

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By Peter Baker and Zolan Kanno-Youngs

Peter Baker and Zolan Kanno-Youngs are White House reporters who have covered Kamala Harris for nearly four years and traveled with her to Europe, Asia, Africa and across the United States.

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She seemed uncertain. “Why?” she asked.

“We need a real leader, and you’re the leader,” Mr. Klain responded.

Ms. Harris asked for time to think about it. She did not want to just give a speech without substance. And she had spent much of the previous year and a half trying to avoid being typecast as the first female vice president. But as the White House began mapping out executive actions to defend access to abortion, she began to see the possibilities and accepted the role.

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Publishing and exposing ports

Explanation.

If you've been following the guides so far, you understand that containers provide isolated processes for each component of your application. Each component - a React frontend, a Python API, and a Postgres database - runs in its own sandbox environment, completely isolated from everything else on your host machine. This isolation is great for security and managing dependencies, but it also means you can’t access them directly. For example, you can’t access the web app in your browser.

That’s where port publishing comes in.

Publishing ports

Publishing a port provides the ability to break through a little bit of networking isolation by setting up a forwarding rule. As an example, you can indicate that requests on your host’s port 8080 should be forwarded to the container’s port 80 . Publishing ports happens during container creation using the -p (or --publish ) flag with docker run . The syntax is:

• HOST_PORT : The port number on your host machine where you want to receive traffic
• CONTAINER_PORT : The port number within the container that's listening for connections

For example, to publish the container's port 80 to host port 8080 :

Now, any traffic sent to port 8080 on your host machine will be forwarded to port 80 within the container.

Important When a port is published, it's published to all network interfaces by default. This means any traffic that reaches your machine can access the published application. Be mindful of publishing databases or any sensitive information. Learn more about published ports here .

Publishing to ephemeral ports

At times, you may want to simply publish the port but don’t care which host port is used. In these cases, you can let Docker pick the port for you. To do so, simply omit the HOST_PORT configuration.

For example, the following command will publish the container’s port 80 onto an ephemeral port on the host:

Once the container is running, using docker ps will show you the port that was chosen:

In this example, the app is exposed on the host at port 54772 .

Publishing all ports

When creating a container image, the EXPOSE instruction is used to indicate the packaged application will use the specified port. These ports aren't published by default.

With the -P or --publish-all flag, you can automatically publish all exposed ports to ephemeral ports. This is quite useful when you’re trying to avoid port conflicts in development or testing environments.

For example, the following command will publish all of the exposed ports configured by the image:

In this hands-on guide, you'll learn how to publish container ports using both the CLI and Docker Compose for deploying a web application.

Use the Docker CLI

In this step, you will run a container and publish its port using the Docker CLI.

Download and install Docker Desktop.

In a terminal, run the following command to start a new container:

The first 8080 refers to the host port. This is the port on your local machine that will be used to access the application running inside the container. The second 80 refers to the container port. This is the port that the application inside the container listens on for incoming connections. Hence, the command binds to port 8080 of the host to port 80 on the container system.

Verify the published port by going to the Containers view of the Docker Dashboard.

Open the website by either selecting the link in the Port(s) column of your container or visiting http://localhost:8080 in your browser.

Use Docker Compose

This example will launch the same application using Docker Compose:

Create a new directory and inside that directory, create a compose.yaml file with the following contents:

The ports configuration accepts a few different forms of syntax for the port definition. In this case, you’re using the same HOST_PORT:CONTAINER_PORT used in the docker run command.

Open a terminal and navigate to the directory you created in the previous step.

Use the docker compose up command to start the application.

Open your browser to http://localhost:8080 .

Additional resources

If you’d like to dive in deeper on this topic, be sure to check out the following resources:

• docker container port CLI reference
• Published ports

Now that you understand how to publish and expose ports, you're ready to learn how to override the container defaults using the docker run command.