Simple Machines Notes PDF

Simple Machines are basic devices that help make work easier by allowing us to apply force in a more efficient way. Simple Machines helps us: lift Pull Increase elevation of heavy things Change the direction of the force Increase the force Split things Faste...

Simple Machines are basic devices that help make work easier by allowing us to apply force in a more efficient way. Simple Machines helps us: lift Pull Increase elevation of heavy things Change the direction of the force Increase the force Split things Fasten things Cut things 6 Kinds of Simple Machines 1. Lever 2. Pulley 3. Wheel and Axle 4. Inclined Plane 5. Screw 6. Wedge 1. LEVER  Fulcrum – a fixed point of a lever Three parts of Lever 1. Resistance force or load – force which the machine operates. It is the load placed on the machines. 2. Effort force – force that operates 3. Fulcrum – a fixed pivot point  Three cases of Lever 1. First Class Levers are ones that have the fulcrum placed between the load (resistance) and effort. 2. Second-class levers are ones that have load in between the fulcrum and effort. 3. Third-class levers are ones that have effort in between the fulcrum and load.  A. Mechanical Advantage 1. AMA - Actual Mechanical Advantage 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑜𝑟𝑐𝑒 AMA = 𝐸𝑓𝑓𝑜𝑟𝑡 𝑓𝑜𝑟𝑐𝑒 2. IMA – Ideal Mechanical Advantage 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑒𝑓𝑓𝑜𝑟𝑡 𝑎𝑟𝑚 𝑑𝑒 IMA=TMA= = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑟𝑚 𝑜𝑓 𝑎 𝑙𝑒𝑣𝑒𝑟 𝑑𝑟 TMA - Theoretical Mechanical Advantage 3. Efficiency – the ratio of output work to the input work expressed in percent. In terms of its mechanical advantage, it is: 𝐴𝑀𝐴 Efficiency = 𝑥 100% 𝐼𝑀𝐴 2. PULLEY  Pulley is a narrow track made by a wheel, which is mounted on a frame. It is a grooved wheel that turns around an axle (fulcrum) It may be fixed, movable, or used in combination. Fixed pulley is attached to something that doesn’t move such as the ceiling or wall. Examples: Pulleys on top of the flagpole to raise and lower the flag, to open curtain or mini blinds, to raise the sail on the boat etc.  FORMULA FOR PULLEY RF IMA = EF RF AMA = EF RF EF = IMA AMA Efficiency (Eff) = IMA 𝑥 100(Expressed as %) 3. WHEEL AND AXLE Wheel and Axle is a simple machine made up of two circular objects that are connected and rotate together. The wheel is the larger, outer component, and the axle is the smaller, central rod that passes through the middle of the wheel. The purpose of this simple machine is to reduce friction and make it easier to move or lift heavy objects. When the wheel turns, the axle turns with it, helping to transfer force and motion. Essentially, the wheel and axle allow objects to roll instead of slide, which makes it easier to transport them. For example, a bicycle uses a wheel and axle system for both the wheels themselves and for the pedals. The axle inside the wheel helps it rotate smoothly when force is applied to the pedals.  EXAMPLES 1.Bicycle: The wheels on a bicycle rotate around the axles when you pedal, allowing the bike to move forward. 2.Car: A car’s wheels are attached to axles, and when the engine provides power, the axles rotate the wheels to move the car. 3.Doorknob: When you turn a doorknob, the axle inside the knob rotates, which in turn rotates the latch mechanism to open or close the door. 3.Doorknob: When you turn a doorknob, the axle inside the knob rotates, which in turn rotates the latch mechanism to open or close the door. 4.Carts and Wagons: Handcarts and wagons use wheels and axles to reduce friction and make it easier to move heavy loads. 5.Fishing Reel: The handle of the fishing reel is connected to an axle, which turns the wheel to spool the fishing line in or out. 6.Clock: In mechanical clocks, the gears connected to the wheel and axle system help drive the hands around the clock face. 7.Trolley or Pulley System: The wheel and axle are used in many lifting devices like a trolley system, where the wheel turns on an axle to move objects up or down. Each of these uses the basic concept of a wheel turning around an axle to make tasks more efficient!  𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑤ℎ𝑒𝑒𝑙 IMA = 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑎𝑥𝑙𝑒 RF AMA = EF AMA Effort (Eff) = IMA AMA = Eff x IMA RF =Eff x IMA EF RF in Newton EF = Eff x IMA 4. INCLINED PLANE  Inclined Plane is a slanting surface connecting a lower level to a higher level. It is a plane resting on a support that makes an angle with the horizontal. Examples: ramp, staircase, ship plank, ladder etc. 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑛𝑒 IMA = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑛𝑒 5. WEDGE  Wedge is a double and movable inclined plane placed back to back. It can be forced between two things to hold them tightly together. Examples: knives and anything with a blade, like scissors and saws, axes, nails, and even teeth etc. 6. SCREW  Screw is an inclined plane that is wrapped around cylinder. One of its function is to fasten things. Some screws are used to make holes. When thinking about screw, think of anything that has thread. The distance between two successive threads of a screw is called pitch (p). 2𝜋𝑙 IMA = 𝑝 WOOD WORKING VISE  EXAMPLE No. 1: Lever 1. A lever, 1 m. long is used to pry up a stone weighing 700N. If the bar is pivoted 0.25 m. from the stone: a. How much force must be applied at the end of the lever? b. What is the AMA? EF W=RF.25 m..75 m. 1 m.  1. A lever, 1 m. long is used to pry up a stone weighing 700N. If the bar is pivoted 0.25 m. from the stone: a. How much force must be applied at the end of the lever? b. What is the AMA? EF W=RF.25 m..75 m. 1 m. Law of the lever states that: Effort Force (EF) x Distance of EF from the pivot = Resistance Force(RF) x Distance of RF from the pivot EF x DEF = RF x DRF  EF W=RF.25 m..75 m. 1 m. EF x DEF = RF x DRF Where: EF = Effort Force or the force applied at the end of the lever (unknown) DEF = distance of EF from the pivot (fulcrum) = (0.75) RF = Weight of the stone (700N) DRF = distance of RF from the pivot (fulcrum) = (0.25)  EF W=RF 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑜𝑟𝑐𝑒 2. AMA = 𝐸𝑓𝑓𝑜𝑟𝑡 𝑓𝑜𝑟𝑐𝑒.25 m..75 m. 700 N 1 m. = 233.33 N 1. Solving for the Force applied at the end of the lever = 3.0000428 EF x DEF = RF x DRF =3 EF x 0.75 = 700N x 0.25 700N 𝑥 0.25 EF = 0.75 EF = 233.33 N - applied force at the end of the lever  Example 2: PULLEY A pulley system has an IMA of 6. It is used to raise 300N barrel. a. What effort must a man exert to do the work? b. If the effort actually applied is 60 N, what is the efficiency of the machine? b. What is the efficiency of the a. What effort must a man machine? exert to do the work? Given: IMA = 6 Given: IMA = 6 RF = 300 N W = RF = 300 N EF = 60 N RF AMA IMA = EF Eff = IMA 𝑥 100(Expressed as %) Rearrange the formula to RF EF = (solve for AMA first) solve for EF IMA RF RF 300N EF = IMA a. AMA = = = 5 E𝐹 60N 300 N 5 EF = = 50 N b. Eff = 𝑥 100 = 83.33% 6 6  EXAMPLE 3: WHEEL AND AXLE A wheel and axle is used to raise a mass of 750 kg. The radius of the wheel is 0.50 mm and the radius of the axle is 0.40 mm. If the efficiency of the machine is 62%, solve for the following: 1. Weight in Newton 2. IMA 3. Applied force (EF) REFER TO YOUR NOTES DURING DISCUSSION  EXAMPLE 4: SCREW What is the efficiency of a vise if its handle is 12 inches long, the screw has 4 threads to an inch and it takes a force of 45 lbs (pounds) on the handle to produce a force of 1,500 lbs between the jaws? 1. Solve for AMA first Given: 1. length (l) = 12 in RF 1,500 𝑙𝑏𝑠 2. Pitch (p) = ¼ in. Since AMA = EF = 45 𝑙𝑏𝑠 3. EF = 45 lbs = 33.33 4. RF = 1,500 lbs 2. Solve for IMA Solutions: IMA= P = 2π𝑙 2 3.1416 (12 in) 1 Formula needed: 4 in. AMA = 301.59 a. Eff = IMA x100% 33.33 3. Eff = 301.59 𝑥100 = 11.05 %  EXAMPLE 5: SCREW In an inclined plane, a force of 80N acts over a distance of 20m to lift a weight of 360N to a height of 40m. What is the efficiency? Solutions: Given: 1. Solve for IMA first 1. RF = 360N 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑛𝑒 Since IMA = 2. EF = 80N ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑙𝑎𝑛𝑒 20𝑚 3. l = 20m = 4𝑚 4. d = 4m IMA = 5 RF 360N 2. AMA = = = 4.5 EF 80N AMA 3. Eff = 𝑥100 = 90 % IMA