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**II. The Simple Machines (p.180-183)**

Machines - Ch. 7 II. The Simple Machines (p ) Lever Pulley Wheel & Axle Inclined Plane Screw Wedge

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A. Lever Lever a bar that is free to pivot about a fixed point, or 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

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**A. Lever Le must be greater than Lr in order to multiply the force.**

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

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**A. Lever First Class Lever can increase force, distance, or neither**

changes direction of force

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A. Lever Second Class Lever always increases force

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A. Lever Third Class Levers always increases distance

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B. Pulley Pulley grooved wheel with a rope or chain running along the groove a “flexible first-class lever” F Le Lr

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**B. Pulley Ideal Mechanical Advantage (IMA)**

equal to the number of supporting ropes IMA = 0 IMA = 1 IMA = 2

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**B. Pulley Fixed Pulley IMA = 1 does not increase force**

changes direction of force

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**B. Pulley Movable Pulley IMA = 2 increases force**

doesn’t change direction

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**B. Pulley Block & Tackle combination of fixed & movable pulleys**

increases force (IMA = 4) may or may not change direction

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**C. Wheel and Axle Wheel and Axle**

two wheels of different sizes that rotate together a pair of “rotating levers” Wheel Axle

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**C. Wheel and Axle Ideal Mechanical Advantage (IMA)**

effort force is usu. applied to wheel axle moves less distance but with greater force effort radius resistance radius

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**Problems Lr Le Lr = 20 cm IMA = Le ÷ Lr Le = 140 cm**

You use a 160 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

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**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

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**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

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**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

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