class notes; 4.26.11. Work and Horsepower NO Quiz TODAY

1. class notes; 4.26.11.Work and HorsepowerNO Quiz TODAY Personal Horsepower Lab Lab Due Wednesday Thursday More information coming tomorrow!! A couple more tickets available.-------------------- Twins Physics Day Early bus stuff Dress for the weather Leave at 8:30 http://www.ftexploring.com/energy/energy-1.htm

2. Lab is due tomorrowToday during work timeFind out answers to questions • Reading Notes (1 page ) • Gravitational Potential Energy • Homework: • Physics: Work (no angles) • Check your understanding of Potential Energy

3. Mechanical Work EqualsZEROno change in speed no workno change in height  no workForce is ┴ to motion no Work W=F*d 1 N m = 1 Joule • W = 0! Carrying a weight corresponds to W = 0. • F is perpendicular to d, θ = 90°: • W = 0.IF you arepushing against an immovable object, d =0 so W = 0!! F 90° d d =0

4. Gravitational Potential Energy Both blocks acquire the same gravitational potential energy, mgh. The same work is done on each block.  What matters is the final elevation, not thepath followed

5. The amount of work done by a force on any object is given by the equation Work = F d cosΘ • F is the Applied force, • d is the displacement • θ is the angle between the F & d Work = F * d Using the force and the distance along the ramp

6. Work and Potential Energy  The work done on the ball gives the ball gravitational potential energy.  Gravitational potential energy = mgh

7. Which Path Requires the Most WORK? • Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain

8. Vertical distance only affects the PE • The PE at the top of each is 30 J, • The work to move up each would be 30 J. • How can this be???? • For Work use Force || to displacement!! Fg UP d Fg UP d Fg UP d

9. Calculations:

10. Watts and Horsepower • James Watt patented the steam engine in 1769. • To sell it, he needed to tell people how many horses it would replace. • He measured how quickly farm horses could do work. • There are few horses that actually produce exactly one horsepower of power.

11. POWER

13. Work, Power and Energy • Notebooks 30 pts + 5 EC for vertical loops • More Equations and Notes today • Tomorrow is the last day to bring in Valleyfair $$$41.50 and permission slip.

14. Work: The Transfer of Mechanical Energy • The baseball pitcher does work on the ball. The ball gains kinetic energy. • To do the greatest possible amount of work, the greatest possible force the greatest possible distance

15. Kinetic energy • The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. • where m = mass of object • v = speed of object

16. Units of work and energy • Like work and potential energy, the standard metric units of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg*(m/s)^2.

17. Analyze the animation and use the principles of work and energy to answer the given questions. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends from a height of 0.60-meters to a height of 0.00 meters. Assume negligible air resistance. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends halfway down a 0.60-meter high hill (i.e., to a height of 0.30 meters). Assume negligible air resistance. • If the mass of the Hot Wheels car was twice as great (0.100 kg), then what would be the speed at the bottom of the 0.60-meter high hill? • If the 0.050-kg Hot Wheels car is brought to a rest over a distance of 0.40 meters, then what is the magnitude of the frictional force acting upon the car?

18. Which Path Requires the Most Energy? • Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain

19. Analyze the animation and use the principles of work and energy to answer the given questions. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends from a height of 0.60-meters to a height of 0.00 meters. Assume negligible air resistance. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends halfway down a 0.60-meter high hill (i.e., to a height of 0.30 meters). Assume negligible air resistance. • If the mass of the Hot Wheels car was twice as great (0.100 kg), then what would be the speed at the bottom of the 0.60-meter high hill? • If the 0.050-kg Hot Wheels car is brought to a rest over a distance of 0.40 meters, then what is the magnitude of the frictional force acting upon the car?

20. Work  Work = Force x DistanceF = 500 pounds (2000 N)D = 8 feet (2.5 meters)----------------------------------- W = 2000 N  x  2.5 m     = 5000 N-m-----------------------------------Alternative unit:  Joule1 N-m = 1 joule (J)

21. Work Work = Force  x  DistanceIf the wall doesn't move,the prisoner does no work.

22.  Energy Work is done on the bow.The work done is storedin the bow and string aselastic potential energy.After release, the arrow issaid to have kineticenergy, 1/2 mv2. Energy is measured in the same units (joules) as work.

23.    Energy Transformation The work done in lifting the massgave the mass gravitationalpotential energy.Potential energy then becomeskinetic energy. Kinetic energy then does workto push stake into ground.

24. Energy Transformation

25.  Power • Power = Work/ Time1 joule / second = 1 watt

26. Total mechanical energy • As discussed earlier, there are two forms of PE discussed in our course - gravitational potential energy and elastic potential energy. Given this fact, the above equation can be rewritten: • TME = PEgrav + PEspring + KE

27. TotalMechanical energystays the same until it hits the water.

28. Work and EnergyHow High Will It Go?The motion of the sled in the animation below is similar to the motion of a roller coaster car on roller coaster track. • As on a roller coaster, energy is transformed from potential energy to kinetic energy and vice versa. Provided that external forces (such as friction forces and applied forces) do not do work, the total amount of mechanical energy will be held constant.

29. Energy Conservation on an Incline • If air resistance is neglected, then it would be expected that the total mechanical energy of the cart would be conserved. The animation below depicts this phenomenon (in the absence of air resistance).

30. Total mechanical energy is constantconservative force  gravity transfers PE-KE • The diagram below depicts the motion of Li Ping Phar (esteemed Chinese ski jumper) as she glides down the hill and makes one of her record-setting jumps.

31. Measurement of Horsepower • The maximum horsepower developed by a human being over a few seconds time can be measured by timing a volunteer running up the stairs in the lecture hall. • If a person of weight W runs up height h in time t, then h.p. = Wh/t X 1/550 ft-lbs/sec. • A person in good shape can develop one to two horsepower. It will be entertaining to the students if the professor tries it too. • Should the person be allowed a running start? http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html http://www.physics.ucla.edu/demoweb/demomanual/mechanics/uniform_circular_motion/index.html

32. Height at A = 60m The car's mass is 500kg. • A roller coaster with two loops and a small hill, see diagram below • In the diagram A is the highest point of the coaster, B is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the ground level, and F is 1/8 of A.

33. HA = 60m m =500kg PE = mgh Speed use KE = ½ m v2 KE = TME (previous) – PE A 60 (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules 294,000J 0 m/s B 45 C 30 D 15 E 0 F 7.5 PE = mgh KE = ½ m v2

34. HA = 60m m =500kg PE = mgh Speed use KE = ½ m v2 KE = TME (previous) – PE A 60 (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules 294,000J 0 m/s B 45 (500(9.8)(45) = 294,000-220,500 = 294,000J 220,500 J 73,500J 17.1 m/s Equation: KE = ½ m v2 Substitute: 73,500J = ½ 500kg v2 X 2 …/ by 500…take √ .. v= 17.1 m/s

35. Mechanical Energy Equations Page 7 section #3

36. W1Force of Gravity pulls down Mechanical Work  PE  KE TME does not change W1 W4 W2 W4

37. The transfers of energy during the 1st Bounce W1 W4 W2 W3

38. W2Force of Gravity pulls down Mechanical Work  PE  KE TME does not change W1 W4 W2 W3

39. W3ball compressed Mechanical Energy lost to HEAT TME does change W1 W2 W4 W3

40. W4Force of Gravity pulls down Mechanical Work  KE  PE TME does not change W1 W4 W2 W3

41. Notice the speed change

43. Missing mechanical energy?? Energyinitial – Energyfinal = Energylost

44. Frictional Work • According to the Cedar Point website the maximum speed of the Magnum XL-200 is 72 mph not 76 mph as we calculated above. • The difference is due to frictional forces acting on the roller coaster cars. • Assuming that the mass of a loaded roller coaster car is 600 kg what is the frictional (non-conservative) work done on the car by the track?

45. Analyze the transfers of energy during the 1st Bounce

46. Work on incline • Answer the following about the above picture: • Draw the three forces acting on the object. • If the object slides down the incline, what work was done with gravity? • What work is done against the motion? • What is the net work done? • Predict the final velocity of the object.

47. Mechanical Energy