1 Energy conservation of energy work, energy, and power machines & efficiency Homework: RQ: 3, 4, 5,10, 12, 13, 15, 18, 30. Ex: 23, 26, 28, 37, 49, 62. Problems: 1, 5, 6.

2 Energy & Work Energy is the capacity to do work. Unit: joule = newton·meter (J = N·m) Work = force x distance (Fd) when force is in direction of motion (or opposite to motion) Ex. 50N pushes distance of 4 meters. W = (50N)(4m) = 200 J /

3 Machines change an applied force by increasing it, decreasing it, or changing its direction. Types: inclined plane, screw, wedge pulley, wheel lever

levers Work input F d = Work output F d Ex. Your hand moves 100m, causes car to rise 0.10m. The force amplification factor is, F F d d = __

5 inclined plane Weight x height change = Force x distance along plane Force along ramp less than Weight Ramp distance greater than height change ADA Standards: Ramp must be at least 12x longer than vertical rise Ex. A 1ft vertical rise requires 12ft of ramp.

ADA Ramp 6

7 Machine Efficiency = (work output)/(energy input) x 100% Ex: 10J are input and 9J are output. Efficiency = (9)/(10) x 100% = 90% Ex: 5J are input and 4J are output. Efficiency = (4)/(5) x 100% = 80% /

Energy of Motion Called Kinetic Energy (KE) KE = ½(mass)(velocity) 2 = ½mv 2. Ex. 2000kg car moving at 2m/s. KE = ½ (2000)(2) 2 = 4000J. 8

9 Work & Energy Work transforms energy from one form to another Work =  KE Ex. Calculate distance 100N must act to move a 2000kg car from rest to 2m/s: Work = Fd = (100N)(d) = 4000 J d = 4000J/100N = 40 meters //

10 Power Power is the rate work is performed Power = work/time = Force x velocity Unit: watt = joule/second = J/s Other Unit: horsepower 1 horsepower = 746 watts /

Energy & Power Energy = power x time Ex. A toy car has 1000 J of energy at full charge. How long can it run at 100 watts? At 10 watts? Time = Energy/power = 1000J/100watts = 10 seconds = 1000J/10watts = 100 seconds/ 11

Energy & Efficiency 1 gallon gasoline has 138,000,000 J Engines only get a fraction of this: Ex. A 25% efficient car gets (0.25)(138,000,000 J) = 34,500,000J out of 1 gallon. A 20% efficient car gets 27,600,000J. 12

Mpg (20% Efficient Engine) Work = Force x distance Ex. 400N for 1600 meters (1 mile) Work = (400N)(1600m) = 640,000J for one mile traveled (1mile/640,000J) Engine gets 27,600,000J per gallon (at constant speed) 13

Stop & Go Mpg Energy is used to speed car, and all is lost to heat when stopping Mpg much less in stop & go conditions / 14

Size, Shape & Mpg Block shape creates more air friction than rounded shape car Larger vehicles experience more air friction Air friction = Shape factor x Frontal Size Ex. At 60mph, an SUV can experience about 4x more air drag than a small car. / 15

Speed & Mpg For a given vehicle, air friction increases with the speed 2. Ex. If you double your speed, the air friction will increase by a factor of 4. / 16

17 Potential Energy … is energy due to position & orientation Ex. Book standing on one end has more potential energy than when lying flat Ex. A ball 1m above floor has more potential energy than when on the floor.

Gravitational Potential Energy = mass x gravity x height Ex. A 2kg ball is 1m above the floor Grav. Pot. Energy = (2kg)(10N/kg)(1m) = 20 joules Ex. A 10kg sack of rice 0.5m above the floor has Grav. Pot. Energy = (10kg)(10N/kg)(0.5m) = 50 joules 18

19 Conservation of Energy Energy cannot be created or destroyed; but is transformed from one form into another – the total amount staying the same. Ex. A falling object loses Gravitational Energy as it falls, but gains an equal amount of Kinetic Energy. /

20 Mechanical Energy = sum of Kinetic and Potential Energy Ex. A glider slides down an inclined air track. The Mech. Energy = KE + mgh = constant as the glider moves to lower heights h. /

21 Summary work = Fd (F along d) work = 0 (F perpendicular to d) Power = work/time = Fv KE = ½mv 2. GPE = mgh work = change in KE total energy always conserved machines & efficiency

7-Ex43 Force 10N object hits ground with. If object sits at rest on ground, Then the answer is 10N (net force = 0, a = 0)

Explain energy conservation Forms of energy: motion, potential, spring, thermal. Slide a book across table, all motion energy disappears. ???? Motion energy  Thermal energy What about your Energy Lab? Potential energy  motion energy

Force & work???? Work is a product of force and distance No distance, no work no force, no work

frictionless slide total energy is 100J, KE = 30J, PE? KE + PE = 100J 30 + PE = 100 PE = 70

calculate KE KE = ½ mv 2. Ex: m = 1000kg, v = 10m/s KE = ½ (1000)(10) 2. = 500(100) = 50,000J

work-energy as long as you really calculate the net work done on an object, that value will always be the change in KE of that object.

28 Net Work net work = sum of all work done on an object net work = (net force*)(d) *parallel to motion //

29 Work-Energy Theorem net work on object = change in kinetic energy of object (KE,final – KE,initial) Ex. 4kg mass falls from rest from height of 1.0m. Work done by gravity = Wh = (4x10)(1) = 40 J net work, 40J = ½mv 2 – 0 40 = ½(4)v = 2v 2. v = square-root of 20 = 4.5m/s