# Chapter 10 Energy Work Machines Work Energy Work

• Slides: 37

Chapter 10: Energy, Work & Machines

Work & Energy: ® Work: ® Force moving through a distance Product of Net Force & displacement W = FNet (d) ® Units: N(m) = Joule ® Work is only done if Force and displacement are in the same direction ® ® Energy: the ability to do work Property of an object to produce a change on itself or the world around it ® Units are also Joules ®

Forms of Energy: ® 2 Basic Forms: ® Potential Energy (PE): energy of position or condition AKA: Stored Energy ® Gravitational PE = m(g)d or Wt(d) ® ® Kinetic Energy (KE): energy of motion ® KE = ½ m(v 2)

Energy Conservation & Calculations: ® Law of Conservation of Energy: Energy can not be created nor destroyed, only changed in form ® PE = Work in = KE = Work out ® Work = F(d) = m(a)d = m(g)d = wt(d) KE = ½ m(v 2) PE = m(g)d With an angle: W = KE = PE = F(cos <) d Finds Horizontal Component of Force

Examples: Sliding: Lifting: Diagonal: F = 800 N d = 40 m m = 60 kg d = 10 m F = 600 N d = 15 m < = 46 O W = F(d) = 800(40) = 32000 J W = m(g)d = 60 (9. 81) 10 = 5886 J W = F (cos <) d = 600(cos 46 O)15 = 6251. 93 J

Assignment: Pg. 261 – 262 #1 - 8 1 a. ) 1. 35 J b. ) 0. 68 J 2 a. ) 28875 J b. ) 57750 J 3 a. ) 603. 3 J b. ) 5892. 315 J c. ) Power = W/t 3. 27 watts 4. ) 4917. 33 J 5. ) 6519. 99 J 6. ) 903 J; -903 J 7. ) 6543. 68 J 8 a. ) 6875 J b. ) – 14821. 54 J

Graphical Analysis of Work & Energy ® Force ® vs. Displacement Graph: Area under the curve = Work Constant Force: Force (N) Displacement (m) Changing Force: Force (N) Displacement (m)

Power ® Power: the amount of work done per unit time Power = work / time P=w/t ® Measured in watts (1 Joule of work per sec. ) ® 1000 watts = 1 kilowatt ® ® If 2 objects do the same work, but one does it much quicker, the one that takes less time, will have more power

Power: ® Power is not strength ® Derivations of Power: ®P = W/t = F(d) / t = m(g)d / t = F (d/t) = F(v) Units: N(m)/s J/s Watts 1000 Watts = 1 Kilowatt

Assignment: Pg. 265 #9 to 23 9. ) 1150 W; 1. 15 k. W 10 a. ) 348 W b. ) 696 W 11. ) 629. 475 W 12. ) 130, 000 N 13. ) 340 s = 5. 667 min. 14. ) 1875 J 15. ) 800 J 16. ) 3462. 92 J (this one’s tricky) 17. ) Individual Answers 18. ) 34531. 2 W 19. ) 4. 4145 J 20. ) 594. 63 kg 21 to 23. ) Individual Answers

A machine is any object that makes work easier ® Remember: Work is the transfer of energy through a distance ® Work = force (distance) ® W = f(d) SI unit Joules ® ® Also Remember: Force is a push or pull ® Force = mass (acceleration) ® F = m(a) SI unit Newtons ® ® This ® means work can also be found… mass (acceleration) distance W = m (a) d

2 types of Machines: Simple & Compound machine: simple machines joined together ® What is a simple machine? Simple machines make work easier by changing the size or direction of the force you use ® Simple machines have only one moving part ® There are 6 types of Simple Machines 1. ) Levers 4. ) Inclined Plane 2. ) Pulleys 5. ) Screws 3. ) Wheel & Axle 6. ) Wedge ® 1, 2 & 3 are related ® 4, 5, & 6 are related ®

A quick look at simple machines: Levers: change direction or amount of force Pulley: change direction and amount of force Wheel and Axle: changes amount of force Incline Plane: changes amount of force

The Basics: Some machines make work easier by changing the amount of force you put into it: Effort Force ® The Force produced by the machine: Resistance Force ® All simple machines MUST obey the laws of conservation ® The work put in must equal the work produced ® ® “Win & Wout” equations ® ® ® Work in = Work out Force in (distance) = Force out (distance) Mass (acc. ) dist. = Mass (acc. ) dist. All 3 equations find the same thin

Mechanical Advantage ® How many times a machine multiplies our effort force Mechanical Advantage (MA) MA = Resistance Force / Effort force MA = FR / FE ® Ex: A machine produces 3000 N when you put 200 N of effort into it. What is the Mechanical Advantage? ® Givens: FR = 3000 N FE = 200 N Unknown: MA Equation: MA = FR / FE Solution: MA = FR / FE MA = 3000 / 200 MA = 15 This means the machine multiplied your effort 15 times

2 types of Mechanical Advantage: ® Ideal Mechanical Adv. (IMA): No friction ® ® IMA = d. E / d. R Actual Mechanical Adv. (MA): Includes friction ® MA = FR / FE ® Keep in Mind: ® We are still doing work (Transferring energy) ® Work in force and distance moved by us ® Work out force and distance moved by machine ® Some simple machines have an MA = 1 ® They only change direction of force (Effort = Resistance)

Levers ® Lever: a bar that pivots on a fixed point called a fulcrum

3 Classes of Levers: ® Class #1: ® Effort at one end ® Fulcrum in the middle ® Load at the other end ® Trade off ® ® ® Gain Force Lose distance Examples: ® ® ® See Saw (teeter totter) Boat Oar ½ of scissors

Class # 2 ® Effort at one end ® Load in the middle ® Fulcrum at other end ® Trade off ® Gain Force ® Lose Distance ® Examples: ® Wheel barrow ® Nut Cracker ® Stapler

Class # 3 ® Load at end ® Effort in the middle ® Fulcrum at other end ® Gain Distance ® Lose Force ® Examples: Arm ® Shovel, Broom ® Baseball Bat ®

We can use math to understand how levers work ® Work in = work out ® FE (DE) = FR (DR) FE effort FR load DE Effort arm DR resistance arm ® Ex: 20 N of effort will lift how much, if the effort arm is 15 m long, and the resistance arm is 5 m long? Givens: Solution: FE = 20 N DE = 15 m FR = ? DR = 5 m FE (DE) = FR (DR) 20 (15) = FR (5) 300 / 5 = FR 60 = FR Unknown: FR You lift 60 N with 20 N of effort MA = 3

Notice the trade off ® If the effort is smaller than the resistance (Load), then the effort arm must be longer than the resistance arm ® The reverse is also true ® Force ® traded for distance You lift more, but not as far

Pulleys ® 2 types: ® Fixed Pulley: attached to an object Load is lifted by the rope ® Only changes direction of force ® No change in force or distance ® Advantage is using gravity ® Since effort = load, MA always = 1 ®

Moveable pulley: ® Not attached, rolls over rope ® Load carried by pulley ® Effort = half of load, MA = 2 ® Load weight shared by each rope ® Trade off less effort, more distance pulled You pull 1 foot of rope (lifting ½ the weight) ® The weight only moves 6 inches ®

Block and Tackle ® Both types can be combined to form a Block & Tackle ® The MA is found by counting support ropes, or number of movable pulleys and multiplying by 2

Wheel and Axle ®A “wheel” revolves around a shaft Ex: Car Wheels, Crank handles, gears ® The “wheel” is always the larger diameter ® ® Effort distance is the radius of the wheel ® Load distance is the radius of the axle ® Since ® we trade distance force Larger wheels = less effort

Gears ® Gears are wheel and axles with teeth cut to prevent slipping Smaller gears = more power ® Larger gears = more speed (less power) ® ® Finding MA for wheel & axle: ® ® We still can use: Load / Effort = MA We can also use: radius of wheel / radius of axle = IMA

Inclined Plane, Screw & Wedge ® Inclined Plane: ramp used to reduce effort needed to lift a load Effort distance: length load is moved ® Resistance distance: height load is above floor ® ® Just like all simple machines: Work in = Work out ® Effort ( Effort Dist. ) = Load (Resistance Dist. ) ®

Longer ramp the less effort needed 100 Work in = Work out 5 m 0 FE (DE) = FR 0 5 25 m (DR) 100 (25) = 500 (5) ® Finding MA: 2500 J = 2500 2 ways again: J Still the same ® MA = Load / Effort results ® IMA = Effort Dist. / Resistance Dist. ® Ex:

Wedge ® 2 inclined planes back to back ® Longer the wedge less force needed Effort Resistance Notice the resistance is split

Screw: ® Inclined plane wrapped around a cylinder You turn the screw many times to get it to move a short distance ® Trade off many turns = less effort ®

Basic Theme: for all simple machines Increase Effort Distance = Less Effort needed ® Increase Resistance Distance = More Effort needed ® All follow: ® Work in = Work out ® Effort ( Effort Dist. ) = Load (Resistance Dist. ) ® ® Mechanical Advantage can be found by Load / Effort Or ® Effort Dist. / Resistance Dist. ®

Pg. 273 #29 to 31& 33 ® 29 a to d. ) Individual Answers ® 30) 5250 N ® 31) 18 ® 33 a to c. ) Individual Answers

Combining Simple Machines ® Compound Machine: 2 or more simple machines joined and working together ® Multi-gear Bicycle: ® Rider has options of changing MA ® Change size of front gear, rear gear or both ® Rear gear larger than front gear = more IMA l l ® Good for acceleration or climbing hills Increases force produced, but must pedal more Rear gear smaller than front gear = less IMA l Good for less pedaling, but must push harder ® Transmissions work the same way

The human body: ®A compound machine Designed as a series of levers, wheel & axles, etc. ® Always has the five components: ® ® Effort (muscles) & Resistance (load) Effort Arm & Resistance Arm (bones) Pivot point or axle (joints)

Efficiency Comparing work in and work out ® Efficiency: the ratio of work output divided by work input expressed as a percentage ® ® ® It’s like grading a machine Efficiency = Work out / Work in (100%) or Efficiency = AMA / IMA (100%) ® High Efficiency work out very close to work in ® ® Almost no energy is lost Low Efficiency Work out much less than work in ® Lots of energy lost somewhere (usually heat & friction)

Pg. 272 #24, 25, 27 & 28 ® 24. ) IMA: 0. 225 ® MA: 0. 214 ® FR = 33. 17 N ® DE = 3. 15 cm ® 25 a. ) IMA: 4. 0 ® b. ) MA: 1. 5 ® c. ) 38. 75 % 27. ) 81. 4 CM 28 a. ) 6. 0 b. ) 166. 67 N