Machines - Ch. 12 Introduction to Machines Work, Power, Energy Mechanical Advantage Simple Machines Compound Machines

W = Fd Work Work transfer of energy through motion force exerted through a distance W = Fd W: work (J) F: force (N) d: distance (m) 1 J = 1 N·m Distance must be in direction of force!

B. Work Brett’s backpack weighs 30 N. How much work is done on the backpack when he lifts it 1.5 m from the floor to his back? GIVEN: F = 30 N d = 1.5 m W = ? WORK: W = F·d W = (30 N)(1.5 m) W = 45 J F W d

B. Work d W F GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after A dancer lifts a 40 kg ballerina 1.4 m in the air and walks forward 2.2 m. How much work is done on the ballerina during and after the lift? GIVEN: m = 40 kg d = 1.4 m - during d = 2.2 m - after W = ? WORK: W = F·d F = m·a F =(40kg)(9.8m/s2)=392 N W = (392 N)(1.4 m) W = 549 J during lift No work after lift. “d” is not in the direction of the force. F W d

Power Power Rate at which work is done; how much work done in a given time W = P t W: work (J) P: Power (Watt) t: time (s) 1 J = 1 N·m Distance must be in direction of force!

Power It takes 100 kJ of work to life an elevator 18 m. If this is done in 20 s, what is the average power of the elevator during the process? GIVEN: W = 100 kJ P = ? t =20 s WORK: P = W÷t P = (100000 J)÷(20) P = 5000 W P W t

Energy ENERGY THERMAL The ability to cause change. MECHANICAL NUCLEAR internal motion of particles ENERGY MECHANICAL NUCLEAR motion of objects changes in the nucleus ELECTRICAL joules (J) CHEMICAL motion of electric charges bonding of atoms

A. Energy Kinetic Energy (KE) energy in the form of motion depends on mass and velocity 80 km/h 50 km/h Which has the most KE? Which has the least KE? 80 km/h truck 50 km/h motorcycle

Kinetic Energy KE = ½ mv2 Kinetic energy depends on speed more than mass

Kinetic Energy What is the kinetic energy of a 44 kg cheetah running at 31 m/s GIVEN: KE = ? m = 44 kg v =31 m/s WORK: KE = ½ (m) (v)2 KE = ½ (44) (31)2 KE = 2.1 x 104 J KE = ½ mv2

A. Energy Potential Energy (PE) stored energy depends on position or configuration of an object Which boulder has greater gravitational PE? What other ways can an object store energy?

PE = mgh Potential Energy m=mass, g=free-fall acceleration, h=height g on earth=9.8 m/s2

Potential Energy PE = mgh A 65 kg rock climber ascends a cliff. What is the climber’s gravitational potential energy at a point 35 m above the base of the cliff GIVEN: PE = ? m = 65 kg g =9.8 m/s2 h= 35 m WORK: PE = mgh PE = (65)(9.8)(35) PE = 2.2 x 104 J PE = mgh

C. Conservation of Energy Law of Conservation of Energy Energy may change forms, but it cannot be created or destroyed under ordinary conditions. EX: PE  KE mechanical  thermal chemical  thermal

C. Conservation of Energy PE  KE View pendulum animation. View roller coaster animation.

C. Conservation of Energy Mechanical  Thermal View rolling ball animations. View skier animation.

A. Machines Machine device that makes work easier changes the size and/or direction of the exerted force

B. Force Effort Force (Fe) force applied to the machine “what you do” Also called Input Force Resistance Force (Fr) force applied by the machine “what the machine does” Also called Output Force

C. Work Win = Fe × de Wout = Fr × dr Work Input (Win) work done on a machine Win = Fe × de Work Output (Wout) work done by a machine Wout = Fr × dr

C. Work Fe × de = Fr × dr Win = Wout Conservation of Energy can never get more work out than you put in trade-off between force and distance Win = Wout Fe × de = Fr × dr

C. Work Win = Wout Win > Wout In an ideal machine... But in the real world… some energy is lost as friction Win > Wout

D. Mechanical Advantage Mechanical Advantage (MA) number of times a machine increases the effort force Fr=resistance force How much force the object has Fe=Effort Force How much force you use MA > 1 : force is increased MA < 1 : distance is increased MA = 1 : only direction is changed

D. Mechanical Advantage A worker applies an effort force of 20 N to open a window with a resistance force of 500 N. What is the crowbar’s MA? GIVEN: Fe = 20 N Fr = 500 N MA = ? WORK: MA = Fr ÷ Fe MA = (500 N) ÷ (20 N) MA = 25 MA Fr Fe

D. Mechanical Advantage Find the effort force needed to lift a 2000 N rock using a jack with a mechanical advantage of 10. GIVEN: Fe = ? Fr = 2000 N MA = 10 WORK: Fe = Fr ÷ MA Fe = (2000 N) ÷ (10) Fe = 200 N MA Fr Fe

D. Mechanical Advantage If you do NOT have forces give, you can solve using distance De=distance of effort (in meters) What you do Dr=Distance of resistance (in meters) What machine does MA > 1 : force is increased MA < 1 : distance is increased MA = 1 : only direction is changed

D. Mechanical Advantage Using a block and tackle pulley, a boy pulls the rope 10 meters to move the weight up 2 meters. Find the MA GIVEN: MA = ? De = 10 m Dr = 2 m WORK: MA = De ÷ Dr MA= (10 m) ÷ (2 m) MA= 5 MA DE Dr

E. Efficiency (Honors) How well a machine works No machine is 100% efficient Many lose efficiency to friction, or energy lost as heat Ex. If a machine is 90% efficient, it means 10% of the energy is lost as another form

E. Efficiency (Honors) Efficiency Formula: Efficiency (%) Eff= Wout x 100 Win Efficiency equal the work out divided by the work in multiplied by 100 Output is always less than the input work

Machines - Ch. 12 II. The Simple Machines Lever Pulley Wheel & Axle Inclined Plane Screw Wedge

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

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.

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

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

A. Lever First Class Lever Fulcrum in the middle can increase force, distance, or neither changes direction of force Examples: seesaws, scissors, pliers

A. Lever Second Class Lever Output force in middle always increases force Example: wheelbarrows, nutcrackers

A. Lever Third Class Levers Input force in middle always increases distance Examples: arms, legs, baseball bats

Three Classes of Levers

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

B. Pulley Ideal Mechanical Advantage (IMA) equal to the number of supporting ropes on the load You only count the end strand when it is pointed up! IMA = 0 IMA = 1 IMA = 2

What is the IMA? =2 =3 =5

B. Pulley Fixed Pulley IMA = 1 (so no mechanical advantage!) does not increase force changes direction of force

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

B. Pulley Systems Block & Tackle combination of fixed & movable pulleys increases force (IMA = >1) may or may not change direction

Pulley Systems

Pulley Systems

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

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 (wheel) resistance radius (axle)

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

D. Inclined Plane Inclined Plane sloping surface used to raise objects h l

E. Screw Screw inclined plane wrapped in a spiral around a cylinder

F. Wedge Wedge a moving inclined plane with 1 or 2 sloping sides

F. Wedge Zipper 2 lower wedges push teeth together 1 upper wedge pushes teeth apart

Problems h Fe l MA Fr Fe = ? IMA = l ÷ h IMA = (3 m)÷(1.2 m) How much force must be exerted to push a 450 N box up a ramp that is 3 m long and 1.2 m high? IMA l h MA Fr Fe GIVEN: Fe = ? Fr = 450 N l = 3 m h = 1.2 m WORK: IMA = l ÷ h IMA = (3 m)÷(1.2 m) IMA = 2.5 Fe = Fr ÷ MA Fe = (450 N)÷(2.5) Fe = 180 N

Compound Machines A machine made up of more than one simple machine Ex: car, pair of scissors, bicycles