Simple Machines

To familiarize students with the different categories of simple machine. Explain how simple machines enhance human capabilities. Work safely and accurately in a variety of experiments. Demonstrate curiosity, exhibit motivation for learning, and use class time effectively. Exhibit and refine inherent personal qualities such as creativity and resourcefulness.

Simple machines make our work easier by providing a mechanical advantage. ◦ We use less effort/do less work to move an object. All simple machines belong to one of two families ◦ The inclined plane family and ◦ The lever family. There are six simple machines ◦ wedge, ramp, screw, lever, wheel and axle, and pulley.

M.A. = Output Force Input Force M.A. = Distance over which effort is applied Distance over which load is moved We know that simple machines make work easier. Mechanical advantage is a measure of how much easier or faster our work has become as a result. Mathematically, this can be calculated as follows: OR

Levers are one of the basic tools that were probably used in prehistoric times. Levers were first described about 260 BC by the ancient Greek mathematician Archimedes ( BC). Effort (E) is the input force which must be supplied by the user or an engine of some kind. Load (R) is the output force which is also the force resisting motion.

Mechanical Advantage (M.A.) L ength from Fulcrum to E ffort = LE L ength from Fulcrum to Load (R) LR M.A. = =

First class lever: The fulcrum is located in the center of the lever arm and the effort and load are at opposite ends. Example: Seesaw Second class lever: With a second-class lever the weight is located in the middle and the fulcrum and the effort or at opposite ends. Example: Wheelbarrow Third class lever: The effort is applied at the middle of the arm and the weight is held at one end while the fulcrum is at the other end. Example: Tweezers

1 st Class 2 nd Class 3 rd Class

A wheel & axle can be made from a 2nd or 3rd class lever. E R Wheel Axle E R Wheel Axle M.A. = Radius (L) to Effort (E) = LE Radius (L) to Load (R) LR

M.A. = Radius (L) to Effort (E) = LE Radius (L) to Load (R) LR Resistance = M.A. * EffortFinds Resistance if the Effort and Mechanical Advantage are known. Torque is a twisting force. The units for torque are typically ft- lbs or inch-lbs. Torque can be calculated using the formula: Torque = Force * radius

Rotary Motion is the circular motion which occurs when the wheel and axle are rotated about the centerline axis. Usually rotary motion is defined in terms of degrees of revolution. Linear Motion is the straight-line motion which occurs when a wheel rolls along a flat surface. The linear distance traveled when the wheel completes one revolution is equal to the circumference of the wheel. Circumference = Pi * Wheel diameter

A pulley is an adaptation of a wheel and axle. A single pulley simply changes the direction of a force. When two or more pulleys are connected together, they permit a heavy load to be lifted with less force. The trade-off is that the end of the rope must move a greater distance than the load.

M.A. = Total number of strands supporting the load

Equations and Terms: Load = M.A. * Effort Finds the Load if the Effort and Mechanical Advantage are known

1. 1. Fixed Pulley is defined when a pulley is attached or fixed to a strong member, which will not move. When a fixed pulley is used the force needed to lift a weight does not change. Notice that it takes 100 N of force to lift a 100N mass (no MA). Only the direction of the force applied is altered. Also note there is no distance advantage either (i.e. 10cm moves the mass 10cm)

2. 2.Movable Pulley splits the work in half. The effort needed to lift 100 N weight is 50 N. The mechanical advantage of a movable pulley is 2. Also note that the trade off is that the rope must be pulled twice as far to lift the object the same distance as in #1. (i. e. 20cm to move the mass 10cm)

3 &4. 3 &4. Block and Tackle is a system of three or more pulleys. It reverses the direction of the effort so that a downward pull can be used to lift an object. For number 3, the mechanical advantage is 3 so that 33 pounds of effort is needed to lift an object weighing 100N. (The distance the rope is pulled has tripled.)

The inclined plane is the simplest machine of all the machines. An inclined plane is a flat sloping surface along which an object can be pushed or pulled. An incline plane is used to move an object upward to a higher position.

Mechanical Advantage (M.A.) M.A. = Length = L Height H Effort = Force M.A. Force = M.A. * E Mechanical Advantage for the Incline Plane Finds the Force if the Effort (E) and Mechanical Advantage are known: This equation is obtained by algebraically manipulating the equation above.

1.During its use, an inclined plane remains stationary, while the wedge moves. 2.With an inclined plane the effort force is applied parallel to the slope of the incline. 3.With a wedge the effort force is applied to the vertical edge (height) incline. M.A. = Length = L Height H

A screw is a combination of two simple machines: 1)an inclined plane 2)a wheel and axle Inclined Plane Wheel and Axel Can be used to change from rotary to straight line (linear) motion.

Equations and Definitions: Screw Pitch is the distance between two adjacent threads on a screw. The formula to calculate pitch is: Pitch = length measured Number of threads per length measured

Equations and Definitions: The Circumference of the screw is calculated using the Geometry formula: Circumference = Pi * Diameter

The formula for the Mechanical Advantage of a screw is: M.A. = Circumference Pitch

Elements of the engineering-design process can be used in short term problem-solving activities: a) learn and practice systematic problem solving, b) develop and apply their creativity and ingenuity c) make concrete applications of mathematics and science skills and concepts.

Challenge Problem To create a device that will fire a ball accurately within a given range. Rules Must be able to fire a projectile (to be specified by the instructor) anywhere within 5’ to 15’ operating range (design adjustability into your device!) Must fit within a 1’x1’ footprint (in “collapsed form”) Cannot utilize high-pressure gases or combustible materials Must be constructed primarily out of materials that are provided and found.