Machines The Simple Machines Lever Pulley Wheel & Axle Inclined Plane Screw Wedge

Objectives Identify the types of levers and pulleys. Calculate ideal mechanical advantage. CLE 3202.4.3 Demonstrate the relationship among work, power, and machines.

A. Simple Machines A machine that does work with only one movement is a simple machine . There are six simple machines: lever, pulley, wheel and axle, inclined plane, screw and wedge.

B. Lever Lever a bar that is free to pivot about a fixed point called a fulcrum “Give me a place to stand and I will move the Earth.” – Archimedes Engraving from Mechanics Magazine, London, 1824 Resistance arm Effort arm Fulcrum

B. Lever – 3 Parts 1. Fulcrum – the fixed point on a lever. 2. Effort arm – part of the lever on which effort force is applied. 3. Resistance arm – part of the lever that exerts the resistance force.

B. Lever 4. There are three classes of levers based on positions of effort arm, resistance arm, and fulcrum.

Lever First-class lever – fulcrum is located between the effort and resistance forces; always multiplies and changes direction of force.

Lever First Class Levers

Lever b. Second Class Lever - resistance force is located between the effort force and fulcrum; always multiplies force.

Lever Second Class Lever

A. Lever C. Third Class Levers effort force is between the resistance force and fulcrum; doesn’t multiply force but does increase distance over which force is applied.

Third Class Levers                          (Hammer hitting nail)

Which Class? Second Class Lever

Levers

Review - Mechanical advantage (MA) is the number of times a machine multiplies the effort force. Calculated: MA = resistance force/effort force

Lever 5. Calculating ideal mechanical advantage (IMA) of a lever – IMA equals length of effort arm divided by length of resistance arm. IMA = L(e) / L(r) 6. MA can be increased by making the resistance arm longer.

Lever Le must be greater than Lr in order to multiply the force. 7. Ideal Mechanical Advantage (IMA) frictionless machine Effort arm length Resistance arm length Le must be greater than Lr in order to multiply the force.

C. Pulley A grooved wheel with a rope, simple chain or cable running along the groove. The axle of the pulley acts as the fulcrum.

1. Fixed Pulley a. A fixed pulley is attached to something that doesn’t move such as ceiling or floor (flagpole) b. Force is not multiplied but direction is changed so IMA = 1

Fixed Pulley c. A fixed pulley is a modified first-class lever.                          

2. Movable Pulley A movable pulley has one end of the rope fixed and the wheel free to move; (construction crane) multiplies force; IMA = 2

Movable Pulley                          

3. Block and Tackle Pulley System of pulleys consisting of fixed and movable pulleys; IMA = number of ropes supporting resistance weight (count the wheels).

4. Pulley - IMA Ideal Mechanical Advantage (IMA) equal to the number of supporting ropes or wheels IMA = 0 IMA = 1 IMA = 2

4. Pulley - IMA

4. Pulley - IMA

Simple Machines D. Wheel and Axle 1. A wheel and axle is a simple machine consisting of a shaft or axle attached to the center of a larger wheel, so that the wheel and axle rotate together.

D. Wheel and Axle Two wheels of different sizes that rotating together A pair of “rotating levers” Modified lever Wheel Axle

D. Wheel and Axle Doorknobs, screwdrivers, and faucet handles are examples of wheel and axles. Doorknob – the larger part is the wheel and smaller part is the axle; crank – lever attached to a shaft. Effort force usually applied to the larger wheel

D. Wheel and Axle IMA = radius of wheel divided by the radius of axle. Note: it is a modified lever form.

D. Wheel and Axle Ideal Mechanical Advantage (IMA) effort force is usually applied to wheel axle moves less distance but with greater force The center of the axle is the fulcrum effort radius resistance radius

Wheel and Axle

Wheel and Axle 5. Gears are modified form of the wheel and axle.

Wheel and Axle Several examples of the wheel & axle are pictured here

Problems Lr Le Lr = 20 cm IMA = Le ÷ Lr Le = 140 cm You use a 140 cm plank to lift a large rock. If the rock is 20 cm from the fulcrum, what is the plank’s IMA? GIVEN: Lr = 20 cm Le = 140 cm IMA = ? WORK: IMA = Le ÷ Lr IMA = (140 cm) ÷ (20 cm) IMA = 7 IMA Le Lr 20cm 160cm

Problems rr re re = 20 cm IMA = re ÷ rr rr = 5 cm A crank on a pasta maker has a radius of 20 cm. The turning shaft has a radius of 5 cm. What is the IMA of this wheel and axle? GIVEN: re = 20 cm rr = 5 cm IMA = ? WORK: IMA = re ÷ rr IMA = (20 cm) ÷ (5 cm) IMA = 4 IMA re rr 20 cm 5 cm

Problems rr re IMA = 6 re = IMA · rr re = ? re = (6)(4 cm) rr = 4 cm A steering wheel requires a mechanical advantage of 6. What radius does the wheel need to have if the steering column has a radius of 4 cm? GIVEN: IMA = 6 re = ? rr = 4 cm WORK: re = IMA · rr re = (6)(4 cm) re = 24 cm IMA re rr rr re

Problems Lr Le Fr = 150 N Le = IMA · Lr Fe = 15 N Le = (10)(0.3) You need to lift a 150 N box using only 15 N of force. How long does the lever need to be if the resistance arm is 0.3m? GIVEN: Fr = 150 N Fe = 15 N Lr = 0.3 m Le = ? MA = 10 WORK: Le = IMA · Lr Le = (10)(0.3) Le = 3 m Total length = Le + Lr Total length = 3.3 m 15N 0.3m ? 150N IMA Le Lr

http://www.edheads.org/activities/simple-machines/index.shtml http://www.mos.org/sln/Leonardo/LeosMysteriousMachinery.html

Objectives Identify the types of levers and pulleys. Calculate ideal mechanical advantage. CLE 3202.4.3 Demonstrate the relationship among work, power, and machines.