Simple Machines

1. Simple Machines Practice #6—Inclined Planes Mr. Burleson geaux15@hotmail.com

2. Agenda • Review • What are Inclined Planes • IMA for Inclined Planes • Simple Machines Practical • Homework

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

4. What is a Wedge? • A wedge is a triangular shaped tool, a compound and portable inclined plane, and one of the six classical simple machines. • It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. • It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces.

5. Wedge Mechanical Advantage • IMA = Length/Width • Or IMA = 1/tanα, where α is the angle of the wedge • Sharp. The more acute, or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical advantage it will yield. • Blunt/Wide. However, in an elastic material such as wood, friction may bind a narrow wedge more easily than a wide one. This is why the head of a splitting maul has a much wider angle than that of an axe. • Higher IMA’s require less force, but will take longer to separate the material

6. What is an Inclined Plane? • An inclined plane is a flat supporting surface tilted at an angle, with one end higher than the other, used as an aid for raising or lowering a load

7. Frictionless Inclined Plane Mechanical Advantage • Frictionless inclined plan means there is no friction between the object and the plan. • Object could be rolling or on wheels • Surface could be low friction/slippery like ice or oil covered • IMA = Length/Rise = 1/sinθ • The longer the ramp the lower the rise, the higher the IMA Where θ is the angle of the plane

8. Friction Inclined Plane Mechanical Advantage • When there is friction between the plane and the load (sliding something up the ramp) some of the work applied is dissipated as heat by friction (Wfrict). • Win = Wfrict + Wout • Ffric = f = μFnormal = mg sinθ , where μ is the coefficient of friction • Fnormal = N = mg cosθ is the normal force between the load and plane Where θ is the angle of the plane

9. Friction Inclined Plane Mechanical Advantage (cont.) Where θ is the angle of the plane If Fi is greater than this equation, load will slide up the ramp If Fi is less than this equation, load will slide down the ramp

10. Friction Inclined Plane Mechanical Advantage (cont.) Where θ is the angle of the plane

11. Example #1 • Mr. Burleson is pushing his 200N frictionless lawn tractor on a flatbed trailer using a 10m ramp. The trailer is 1m off the ground • The IMA for a frictionless plane is IMA = Length/Rise = 10m/1m = 10 • Mr. Burleson has to push 200N / 10 = 20N to push the tractor up the ramp • If the ramp was half as long, the IMA = 5m/1m = 5 and he would push it 200N/5 = 40N. • If the ramp was twice as long, the IMA = 20m/1m = 20 and he would push it 200N/20=10N

12. Example #2

13. Example #3

14. In Practice Quiz • Explain what would have happened in the Example #2 if the ramp was at the Angle of Repose (yes this may be an illegal question)? • Explain what would have happened in the Example #3 if the ramp was at the Angle of Repose? • If Mr. Burleson put graphite or some other lubricant on the ramp, what would have been the effect on Examples 1, 2, and 3?

15. Practical • Now practice with your lever device and see if you can get within 99% accuracy of the actual ratios • Do not time until you have achieved 99% accuracy 3 times in a row

16. Homework #1 Wedges • Explain how the conservation of energy is used to solve for IMA for both friction and frictionless planes (see Wikipedia for some good ideas). Must be written in student’s handwriting and not copied. • Use the homework generator and do Level 1-5 tabs