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Machines - Ch. 7 II. The Simple Machines (p.180-183) 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 Effort arm Resistance arm Fulcrum

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A. Lever Ideal Mechanical Advantage (IMA) frictionless machine Effort arm length Resistance arm length L e must be greater than L r 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 LeLe LrLr F

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B. Pulley Ideal Mechanical Advantage (IMA) equal to the number of supporting ropes IMA = 0IMA = 1IMA = 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 doesnt 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 You use a 160 cm plank to lift a large rock. If the rock is 20 cm from the fulcrum, what is the planks IMA? GIVEN: L r = 20 cm L e = 140 cm IMA = ? WORK : IMA = L e ÷ L r IMA = (140 cm) ÷ (20 cm) IMA = 7 IMA LeLe LrLr 20cm 160cm

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Problems 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: r e = 20 cm r r = 5 cm IMA = ? WORK : IMA = r e ÷ r r IMA = (20 cm) ÷ (5 cm) IMA = 4 IMA rere r 5 cm 20 cm

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Problems 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 r e = ? r r = 4 cm WORK : r e = IMA · r r r e = (6)(4 cm) r e = 24 cm IMA rere r r rere

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Problems 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: F r = 150 N F e = 15 N L r = 0.3 m L e = ? MA = 10 WORK : L e = IMA · L r L e = (10)(0.3) L e = 3 m Total length = L e + L r Total length = 3.3 m IMA LeLe LrLr 0.3m ? 150N 15N

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