Machines

1. Machines Practice #4—Wheel and Axle Mr. Burleson geaux15@hotmail.com

2. Agenda • Review • What are wheel and axles • IMA for different types of wheel and axles • Simple Machines Practical • Homework

3. Basics of Simple Machines • Lever • Inclined Plane • Wheel and Axle • Wedge • Pulley • Screw (not included in Machines [B])

4. Types of Pulleys • Three major types • Fixed: A fixed pulley has an axle mounted in bearings attached to a supporting structure. A fixed pulley changes the direction of the force on a rope or belt that moves along its circumference. Mechanical advantage is gained by combining a fixed pulley with a movable pulley or another fixed pulley of a different diameter. • Movable: A movable pulley has an axle in a movable block. A single movable pulley is supported by two parts of the same rope and has a mechanical advantage of two. • Compound: A combination of fixed and a movable pulleys forms a block and tackle. A block and tackle can have several pulleys mounted on the fixed and moving axles, further increasing the mechanical advantage.

5. Types of Pulleys • Three major types • Fixed: A fixed pulley has an axle mounted in bearings attached to a supporting structure. A fixed pulley changes the direction of the force on a rope or belt that moves along its circumference. Mechanical advantage is gained by combining a fixed pulley with a movable pulley or another fixed pulley of a different diameter. • Movable: A movable pulley has an axle in a movable block. A single movable pulley is supported by two parts of the same rope and has a mechanical advantage of two. • Compound: A combination of fixed and a movable pulleys forms a block and tackle. A block and tackle can have several pulleys mounted on the fixed and moving axles, further increasing the mechanical advantage.

6. Pulleys linked by a circular chain or belt • Below is a pulley and belt system, which operates like a Wheel and Axle, but is classified a pulley system • Pulleys have different axles • Motion is circular/angular not linear • The IMA is dependent upon the ratio of the wheels/pulleys versus the number of lines connecting • One wheel/pulley is the driver and one is the driven

7. What is a Wheel and Axle • Wheel and Axle is a simple machine that is generally considered to be a wheel attached to an axle so that these two parts rotate together in which a force is transferred from one to the other. • The IMA is caused by the difference in radius between the wheel and axle • Either the Wheel or Axle may be the driving force

8. Wheel and Axle (cont.) • The earliest well-dated depiction of a wheeled vehicle (a wagon—four wheels, two axles) is on the Bronocice pot, a ca. 3635–3370 BC ceramic vase, excavated in a Funnelbeaker culture settlement in southern Poland • The oldest known example of a wooden wheel and its axle was found in 2002 at the Ljubljana Marshes some 20 km south of Ljubljana, the capital of Slovenia. According to radiocarbon dating, it is between 5,100 and 5,350 years old. The wheel was made of ash and oak and had a radius of 70 cm and the axle is 120 cm long and made of oak

9. Wheel and Axle Mechanical Advantage • The force applied to the edge of the wheel is less than the force applied to edge of the axle. • If you have a wheel and axle, each with their own radii, here is the formula • Notice the torques are equal.

10. Gears are also a Wheel and Axle type of machine • A gear or cogwheel is a rotating machine part having cut teeth, or cogs, which mesh with another toothed part in order to transmit torque • Usually the teeth on the one gear of identical shape, and often also with that shape (or just width) on the other gear. • Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine.

11. Gears are also a Wheel and Axle type of machine (cont.) • Geared devices can change the speed, torque, and direction of a power source. The most common situation is for a gear to mesh with another gear; however, a gear can also mesh with a non-rotating toothed part, called a rack, thereby producing translation instead of rotation. • This would not be considered a wheel and axle. (it is considered a screw)

12. Wheel and Axle IMA using Gear Ratio • The torque times the angular motion is the same on each ideal gear (this is different than the other example because the gears are moving). • The larger gear rotates slower (angular motion), but has more torque • The smaller gear rotates faster (angular motion), but has less torque • The Gear Ratio (R) is also known as the Torque Ratio and is equal to the IMA (mechanical advantage) of two meshing gears is given by (where A is the input and B is the output)

13. Example #1 • The drive axle of a Wheeled Vehicle is pulled by a string with 10 N force. • The drive axle has a 0.1 cm radius • The wheel has a 5 cm radius • Since the drive force is on the axle, the IMA to the right is reversed. • The IMA = Fwheel / Faxle = raxle /rwheel = 0.1 cm/5 cm = 0.02 • If the wheel was driving the force (like with a hand crank) • The IMA = Faxle /Fwheel = rwheel/raxle = 5 cm/0.1 cm = 50

14. Example #2 • A windlass is shown and is used to lift a 20 N bucket of water • If the wheel has a radius of 1 m and the cylinder has a radius of 10 cm • The IMA = Faxle /Fwheel = rwheel/raxle = 1 m/0.1 m = 10 • The Faxle= 20 N, Fwheel= Faxle / IMA = 20 N / 10 = 2 N

15. Example #3 • On board a ship, they are using a capstan to raise the 1,000 N anchor. • The Capstan bars are pushed by a single crewman 2 m from the center of the axle • The chain is wrapped around the Capstan where the radius is 30 cm • How hard does the crewman have to push? • The IMA = Faxle /Fwheel = rwheel/raxle = 2 m/0.3 m = 6.67 • The Faxle= 1,000 N, Fwheel= Faxle / IMA = 1,000 N / 6.67 = 150 N • If a second person pushes opposite at the same distance, they only need to push 75 N

16. In Practice Quiz • Do a practice test (several can be found at www.scioly.org • For this first one use your binders, but no teamwork just yet

17. Homework #4 Wheel and Axle • Find a website with different types of gears other than the ones presented in class, print that out to share with the team. • Do Homework Generator Level 1 Wheel Axle and any other areas you had problems on the sample test • Finish your lever so we can do some measurements practicing