Machines Ch 7 II The Simple Machines p

Machines - Ch. 7 II. The Simple Machines (p. 180 -183) Lever t Inclined Plane t Pulley t Wheel & Axle t Screw t Wedge t

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

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

A. Lever u First Class Lever l can increase force, distance, or neither l changes direction of force

A. Lever u Second Class Lever l always increases force

A. Lever u Third Class Levers l always increases distance

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

B. Pulley u Ideal Mechanical Advantage (IMA) l equal to the number of supporting ropes IMA = 0 IMA = 1 IMA = 2

B. Pulley u Fixed Pulley l IMA =1 l does not increase force l changes direction of force

B. Pulley u Movable Pulley IMA = 2 l increases force l doesn’t change direction l

B. Pulley u Block & Tackle l l l combination of fixed & movable pulleys increases force (IMA = 4) may or may not change direction

C. Wheel and Axle u Wheel and Axle l two wheels of different sizes that rotate together l a pair of Wheel “rotating levers” Axle

C. Wheel and Axle u Ideal Mechanical Advantage (IMA) l l effort force is usu. applied to wheel axle moves less distance but with greater force effort radius resistance radius

Problems u 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: WORK: Lr = 20 cm Le = 140 cm IMA = ? Le IMA = Le ÷ Lr IMA = (140 cm) ÷ (20 cm) IMA = 7 20 cm IMA Lr 160 cm

Problems u 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: WORK: re = 20 cm rr = 5 cm IMA = ? IMA = re ÷ rr IMA = (20 cm) ÷ (5 cm) IMA = 4 re IMA 5 cm 20 cm rr

Problems u 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: WORK: IMA = 6 re = ? rr = 4 cm re = IMA · rr re = (6)(4 cm) re = 24 cm re IMA rr rr re

Problems u 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. 3 m? GIVEN: WORK: Fr = 150 N Fe = 15 N Lr = 0. 3 m Le = ? MA = 10 Le = IMA · Lr 15 N Le = (10)(0. 3) Le = 3 m Total length = Le + Lr Total length = 3. 3 m 0. 3 m ? Le IMA 150 N Lr