1 5 Work & Energy Homework: 2, 6, 9, 11, 27, 33, 37, 45, 49, 53, 75, 81, 85, 101.

2 Energy & Work Energy is the capacity to do work, Energy is position & speed dependent 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

Energy of Motion Called Kinetic Energy (K) K = ½(mass)(velocity) 2 = ½mv 2. Ex. 2000kg car moving at 2m/s. K = ½ (2000)(2) 2 = 4000J. Position Dependent Energies are called Potential Energies “U” / 7

Gravitational Potential Energy U = weight x height (mgh) 1kg at 1m height: U = (1kg)(9.8N/kg)(1m) = 9.8J Energy released in falling /

Elastic Potential Energy U = average force x distance Spring compressed 1m with 1N: U = (½ N)(1m) = ½ J k = spring constant = force/distance U = (½kx)x = ½kx 2

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

Vehicle 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

Vehicle Frictional Work = Total Frictional Force x distance Ex. 400N friction for 1600 meters (1 mile) Work = (400N)(1600m) = 640,000J for one mile traveled /

Mpg

Ex. Mpg 20% Efficiency, f = 400N Engine gets 27,600,000 J/gal Frictional Work/Mile = 640,000J/mile = 43 mpg (at constant speed) 15

Work & Force Work is energy transferred by part of force in line of motion Ex. Force 60° above path of motion

Work Example mg mgsin  d mg h  (mgsin  )d = mg(dsin  ) = mgh Moving down an inclined plane

Work Energy Theorem Let direction of motion be +x

19 Example A 20kg mass is moving at 5m/s. 250J of work (net) are done on it. What is its final speed?

20 A 20kg block moving at 5m/s experiences 50N of frictional force. What is the block’s speed after moving 3m?

21 Conservation of Energy Individual energy levels change. Net energy is constant. E =  K +  U = constant Ex. Falling object’s kinetic energy increase equals its loss of grav. potential energy Ex. Arrow’s kinetic energy increase equals loss of elastic potential energy /

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23 EnergyE1E2E3 Kinetic0½mv PE-g00mgh PE- spring ½kx 2 00 Totals  ½kx 2 ½mv 2 2 mgh

24 Energy (i) h (f) y Kinetic0½mv 2 PE-gmghmgy Totals  mgh½mv 2 + mgy Energies and speeds are same at height y Accelerations at y are not same

25 EnergyEiEf Kinetic½mv i 2 0 U-g00 Thermal0fksfks Totals  ½mv i 2 fksfks Ex. Sled slides to a stop s

26 A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie- frame type diagram of the motion is shown below. TypeE1E2E3E4E5 gravita- tional mg(1)000mg(1/2) kinetic0½ m(v2) 2 0½ m(v4) 2 0 elastic00PE-elastic00 thermal00PE-thermal

27 Terminology E: total energy of a system E-mech = total energy minus the thermal energy E-mech = E – U th. Mech. Energy conserved in a frictionless system

28 Power: The time rate of doing work. SI Unit: watt, W = J/s Example: How much average power is needed to accelerate a 2000kg car from rest to 20m/s in 5.0s? work =  KE

29 Another equation for Power: Ex: A car drives at 20m/s and experiences air- drag of 400N. The engine must use (400N)(20m/s) = 8,000 watts of engine power to overcome this force. 8,000 watts = 10.7 hp.

30 Summary Energy: Kinetic + Potential + Thermal, is conserved. Mech. Energy: Kinetic + Potential, conserved w/o friction. Work is energy transfer (+ or -) Power is rate of energy transfer

31 Horsepower: 1 hp = 746 watts For the previous example:

32 What size electric motor is needed to raise 2000lbs = 9000N of bricks at 10cm/s? Minimum Power: P avg = Fv avg = (9000N)(0.1m/s) P = 900 W = 1.2 hp

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36 Similar to gram bullet moves at 200m/s and goes 10cm into a tree. What is the average force on the bullet? Tree? Wnet on bullet = -Fd = change in K Change in K = 0 – ½ (0.003kg)(200)(200) -F(0.1m) = - 60Nm F = 600N

37 By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J Calculate v2: (use 1st and 2nd columns) mg(1) = ½ m(v2)2. g = ½ (v2)2. v2 = 4.43m/s Calculate PE-thermal: (use 1st and 5th columns) mg(1) = mg(1/2) + PE-thermal mg(1/2) = PE-thermal PE-thermal = 9.8J

38 Calculate PE-elastic: (use 1st and 3rd columns) PE-elastic + PE-thermal = mg(1) PE-elastic = 19.6 PE-elastic = 9.8J Calculate v4: (use 1st and 4th columns) ½ m(v4)2 + PE-thermal = mg(1) ½ m(v4) = 19.6 ½ m(v4)2 = 9.8 (v4)2 = 2(9.8)/2 v4 = 3.13m/s