# Simple Machines

### Objectives

1. To list and describe the six basic simples machines.

2. To be able to calculate the mechanical advantage of a lever, wheel and axle and inclined plane.

3. To explain the differences between the three types of levers, and two types of pulleys.

 This section addresses, in whole or in part, the following Georgia GPS standard(s): S8P3.  Students will investigate relationship between force, mass, and the motion of objects. c. Demonstrate the effect of simple machines (lever, inclined plane, pulley, wedge, screw, and wheel and axle) on work.

 This section addresses, in whole or in part, the following Benchmarks for Science Literacy: Tools are used to do things better or more easily and to do some things that could not otherwise be done at all. In technology, tools are used to observe, measure, and make things. Throughout all of history, people everywhere have invented and used tools. Most tools of today are different from those of the past but many are modifications of very ancient tools. Changes in speed or direction of motion are caused by forces. The greater the force is, the greater the change in motion will be. The more massive an object is, the less effect a given force will have.

 This section addresses, in whole or in part, the following National Science Education Standards: People have always had problems and invented tools and techniques (ways of doing something) to solve problems. Trying to determine the effects of solutions helps people avoid some new problems. Tools help scientists make better observations, measurements, and equipment for investigations. They help scientists see, measure, and do things that they could not otherwise see, measure, and do.

Machines

A machine is any mechanical or electrical device that uses energy to perform or help perform a human task.

Mechanical machines are popular because they save us work.  More precisely, they multiply our ability to do work.  They increase the force we need, add some energy, do work we couldn’t do before.  I’m not talking about machines like computers or televisions or toasters.  These are not mechanical machines.  But they HAVE some mechanical machines in them.  We shall see later if you can recognize them.

Vocabulary

Lever

Pulley

Wheel and Axle

Fulcrum

Inclined plane

Wedge

Screw

Types of Machines

There are two kinds of mechanical machines, simple and compound

As you might guess, a simple machine is a single mechanical device.

A compound machine uses more than one simple machine in it.

Machines usually multiply force. The amount by which a machine can multiply a force is called the machine's mechanical advantage.  Whether a machine is useful depends on whether it gives us more mechanical ‘strength’ (mechanical advantage, or M.A.) than doing the work ourselves.  Can we raise a heavier load up in the air better with a machine?  If so, then it is useful and has an advantage of some value times more than if we did it ourselves.

Mechanical advantage - the ratio of force output to force input.  Since both forces are in Newtons, the units cancel  (unitless).

The work a machine does is called work output.  The energy or work put in the machine is called work input.

The work output of a machine can never exceed the work input.

Efficiency = percentage of input work that is converted to usable output of work.

Efficiency = work output/work input

Machines help us by taking the input work (energy/forces) we provide and get some more force or energy out than we supplied.  Uh, doesn’t that violate the law of conservation of energy?  No, because the extra force comes at a price.  Remember that work is a function of force AND distance.  If we get more force out, it comes at a sacrifice of some distance during which the force will be applied.  In actual fact, the work in and the work out of the machine are equal.  But the forces in and out, and distances applied in and out, will not be.  One increases, the other decreases to compensate.  We have to decide if we want more force out or greater distance to apply a smaller force.

Types of Simple Machines

There are six basic simple machines, in two types or families.

The lever family consists of the simple lever, the pulley, and wheel and axle.  All redirect the energy or work done into a different direction than what the input work was entered through rotation.

The inclined plane family is the simple inclined plane, the wedge, and the screw.  This family also redirects the work, but into a perpendicular direction to the direction of motion of the input work.

The Lever Family

Levers

Levers work by having an input force applied at some distance (called the rigid arm) from a pivoting point, called the fulcrum, and some force comes out at another distance from the fulcrum (a second, rigid arm value).

Actually, there are three kinds of levers.

1.  The first kind is the seesaw or hammer type

The input force is at distance from the fulcrum, usually long, and the output is on the other side of, but much closer to, the fulcrum. You get an increased amount of force out but usable only over a shorter distance.  This is why you hold the hammer at the greatest handle length, and the claw to pull the nail is short.  You need not work so hard to pull out a nail this way.  You get a lot of force at the claw part but the handle moves a great deal more distance.

The Mechanical Advantage of a lever is the input distance (i.e. hammer head to end of handle) divided by the output distance (hammer head to the “V” bottom where the nail is caught).  If the handle is 8 times longer than the nail catcher, you have an M.A. of 8; the higher the M.A., the better.

Examples of levers.  Which of these is a compound machine?  What other type of machine does it have in it?

Archimedes said, “Give me a big enough lever and I can move the world!”  Well, don’t have one but I’ve got one here in which you can move an obelisk like the Washington Monument….. http://www.pbs.org/wgbh/nova/egypt/raising/lever.html

Set up a first class lever using a pencil, board, or any other long object.  Use another one to act as the fulcrum.  Use the level to lift up a pile of something (books, flat rock, computer printer, whatever).  Then change the fulcrum location, thus changing the rigid arm and see how the amount of force needed by you changes.  Confirm the relationship that the longer the output rigid arm, the more input force you need.  If you have an adequate spring scale, pull on your lever with it and measure the amount of force you need for different distances.  See if halving the distance doubles or halves the force required.

2.  The second class of lever might be called the wheelbarrow type

It has the fulcrum at one end of the lever and the input is at the other end. The output force is in the middle. In a wheelbarrow, you lift up the load of dirt in the middle by lifting up the end of the handles  The fulcrum is the wheel.  Doors are second class levers too, since we push on the door handles to open them, the fulcrum is the hinges.

Wheelbarrow

3.  The third kind of lever is like the second class, but input and output forces are reversed.  Instead of inputting at the end and outputting work in the middle like the wheelbarrow, we input the work force in the middle and get a smaller output force at the end.

Your arm is a third class lever.  The force is generated by muscles with a lot of force but little distance in ‘rigid arm length’ in the middle of arm around the elbow and you raise your wrist and hand a lot but with less energy available to use.

Another such lever is a sweep broom.  If your hand on the top is the fulcrum, your other hand is in the middle pulling the broom towards you, and the output force is found through the bristles on the floor.

The third class of lever - your arm

Pulleys

Pulleys are like levers but the forces in and out are changed by rotation around the center of a pulley wheel, which acts like a fulcrum. For pulleys, the mechanical advantage is calculated by asking how many of the ropes on all sides of all pulleys in the system are pulling up against gravity.

Here is a website to play with various combinations of pulleys and compute mechanical advantages.  http://www.phy.ntnu.edu.tw/java/wheelAxle/pulley.html

An ‘over the top” fixed, hanging pulley has no mechanical advantage.  The force in and the force out are identical, at the same arm length (the pulley diameter) but the directions are merely changed. You pull with 150 N on one side of the rope over the pulley and 150 N are used to pull up the bucket hanging on the other end of the rope. For a fixed pulley, there is only one rope being pulled against gravity, the one you pulled.  Therefore the M.A. is 1, the same as if you lifted a bucket with your own hands.

Fixed pulleys

A moving pulley that rides on the rope instead of having the rope go over it has a mechanical advantage of 2 because the rope you pull on to lift the pulley and its load carries only half the weight of the load.  But you can only move it half as much a distance upwards. For the moving pulley, it is two, the two sides of rope on either side of the pulley.  For other combinations of these, it can be higher.

Fixed pulley

By combining fixed and movable pulleys, you can get even higher amounts of mechanical advantage.

Movable pulley on a crane

Find or make two fixed pulleys.  Hang them some distance apart but at the same height from the floor.  Put a movable pulley between them.  Tie a string to the hook of the movable pulley, pull the string over one fixed one, under the free one, and finally over the second fixed pulley.  Hang a heavy mass to the free pulley and a slightly less massive weight to the free end of the string.  Predict what should happen.  {Time passes}  Now let go of the masses.  If you predicted the bigger one will move up, you win!  And, you’ve shown why pulleys are so helpful;  a little guy can lift up a heavier big guy with pulleys!

Wheel and Axle

Finally, a wheel and axle is a pulley connected to shaft.  The wheel just rotates.

The input force can be on the outside rim of the wheel while the output can be the shaft itself or a rope attached to it.  You get more force out this way.

It is like a bicycle pedal.  You turn with plain old foot power around the outside of the wheel, a long lever arm connected to the shaft.  The small shaft turns a smaller circumferential gear.  This gear has more power to turn the chain and the big wheel than if you were to pedal power the rear wheel all by yourself.  It trades rigid arm length for increased power.  The mechanical advantage can be calculated by the ratio of the outer wheel rim where force is applied divided by the smaller shaft diameter where force comes out.

The bicycle pedal, showing gear and chain (a pulley connected to a shaft)

You can also have the input force from the shaft and output force around the wheel rim.

A car steering wheel is also a wheel and axle.  You apply a little force to turn it and the shaft of the steering wheel activates the wheel devices to turn the tires with a lot of force but over the small shaft diameter.

More examples of the wheel and axle

The Inclined Plane Family

The Inclined Plane

An incline plane redirects a horizontal pushing force into a vertical force that raises a mass upwards.  The longer the base of the incline compared to the vertical height the mass is being raised, the more mechanically advantageous.  You still need the same amount of work it takes to raise the mass upwards (a box, you, a wheelchair) but you do it with less force over a longer horizontal distance than just back-breaking lifting!

Inclined planes

2.3.2      Wedge issues

A wedge is TWO inclined planes back to back.  Instead of pushing an object up the incline, you push the inclines into an object!

Nails, knives, razors, axes, hatchets, shovels, the points of a fork, even a shark's tooth, are all wedges.  Like simple planes, the advantage increases with ‘sharpness’.  (You knew that; it is why you make sure your knives are sharpened when you cut the turkey.)

Types of wedges

Screws

Screws are inclined planes wrapped around a cylinder.  They also act like a wedge albeit with just one edge to separate things.  The more gentle the curving, the less force needed but it is needed over a longer distance.  If you have tighter curving, you need more force and move less distance as the screw turns.

Images courtesy of NASA

Table of Simple Machines

 Simple Machine Description What it does Examples The Lever Family Lever A stiff structure that pivots on a support called a fulcrum Lifts or moves loads Shovel Nutcracker Seesaw Crowbar Elbow Tweezers Bottle opener Pulley A grooved wheel with a rope or cable around it Moves things up, down, or across Flag pole Crane Curtain rod Tow truck Mini-blind Bicycle chain Wheel and axle A wheel that turns about an axle through its center; both wheel and axle move together Lifts or moves loads Ferris wheel Bicycle pedal Bicycle wheel Car wheel Wagon wheel Doorknob Pencil sharpener Wind-up hose Inclined Plane Family Inclined plane A sloping surface connecting a lower level to a higher level Things move up or down it Wheelchair ramp Slide Stairs Escalator Slope Wedge An object with at least one slanting side ending in a sharp edge Cuts or spreads an object apart Knife Pin Nail Chisel Ax Hatchet Fork Snowplow Front of a boat Screw An inclined plane wrapped around a cylinder Holds things together or lifts Screw Jar lid Vise Bolt Drill Corkscrew

Compound Machines

Compound machines are those that use two or more simple machines in combination.  Most complex mechanical devices use more than one simple machine to make themselves work.  Often the output force of one machine becomes the input force for the next one.

What simple machines can you find in a vice?

How many simple machines can you identify in this compound machine?  There are at least three different ones.

A fantastic classroom example is a bicycle!  In my classes, I have all students draw a bicycle and label the locations with the type of simple machine they find.  Examples:  The handlebars are a wheel and axle.  The pedals, too.  Levers are found with the hand brakes.  The wheels are wedges when they are moving through water or loose dirt.

Bicycle (left) and hand break lever (right)

Look around your room/classroom.  Where can you find simple machines?  There’s a pulley in your window blinds.  Screws and wedges and wheel and axle in your hand-cranked pencil sharpener.  Doors are levers.  Door knobs are wheel and axles.  Thumbtacks are wedges.  How many can you find?

Review Questions

1. List and describe the six basic simple machines.

2. What is the mechanical advantage of a 2-meter bar in which the fulcrum is 25-cm from the edge?

3. You have to push a wheelchair-bound friend up a ramp that is 2m high.  He and the chair weigh 1000N.  You could lift him; how much energy would you need?  Now, if the ramp is 10m long, what is the mechanical advantage of the ramp?  Use this to determine how much force you now need to push him up the ramp.

4. In the above example, it took you 10 seconds to push him up the ramp.  By himself, your friend took 30 seconds.  If it took 100 W of work to do it, what would be your amounts of power?

5. Explain the differences between the three types of levers, and two types of pulleys.

Define

Lever

Pulley

Wheel and Axle

Fulcrum

Inclined plane

Wedge

Screw

Content provided by Larry Krumenaker, Georgia Perimeter College

Photos courtesy of Pamela J. W. Gore

Screw images courtesy of NASA,  http://www.grc.nasa.gov/WWW/K-12/Summer_Training/KaeAvenueES/The_Screw.html

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created March 6-8, 2007
Modified May 19, 2007
Modified May 27, 2007