1 / 67

Work, Energy, and Power

Work, Energy, and Power. Work. What is Work and Energy?. Energy(E)- the ability to do work Work (W)- A change in energy (ΔE) or the product of Force and distance (d) W= Fd Work is only being done when components of the applied force are parallel to the displacement

kacia
Télécharger la présentation

Work, Energy, and Power

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Work, Energy, and Power Work

  2. What is Work and Energy? • Energy(E)- the ability to do work • Work (W)- A change in energy (ΔE) or the product of Force and distance (d) • W=Fd • Work is only being done when components of the applied force are parallel to the displacement • Both are scalar and are measured in joules • 1 joule=kg m2/s2 or 1 joule=N*m

  3. When is work being done? • If a hold a 30 kg object at a height of 1.5 meters is work being done? • I am exerting energy…. • Work is NOT being done on the OBJECT, work is being done on muscles, but not the object • The distance that the object has moved is zero so no work is done • W=Fd W=F0

  4. Example • If the same 30 kg object was pushed to the right with an acceleration of 2m/s2 for 2.0 meters, how much work is done on the object? • W=Fd • Remember F=ma • M=30 kg • a=2 m/s2 • d=2.0 m • W=? • F=ma • F=30(2) = 60N • W=Fd • W=60(2) =120 J

  5. Example • If I were to lift the 30.0 kg object up off the ground to a height of 1.5 m, how much work is done on the object? • When an object is being lifted against gravity, use g for the acceleration (9.8 m/s2) • W=mgd • m=30 kg • g=9.8 m/s2 • d=1.5 m • W=? • W=30(9.8)(1.5) W= 440 J

  6. Clicker Question • A 3.0 kg pineapple is held 1.2 m above the floor for 15 s. How much work is done on the pineapple? • A)0.25 J • B)54 J • C)35 J • D) 0 J

  7. Clicker Question • A 10.0 kg pumpkin is moved horizontally 5.00 m at a constant velocity across a level floor using a horizontal force of 3.00 N. How much work is done in moving the pumpkin? • A) 30 J • B) 294 J • C) 15 J • D) 0 J

  8. Example- Honors • A 50.0 kg banana box is pulled 11.0 m along a level surface by a rope. If the rope makes an angle with the floor of 35oand the tension in the rope is 90.0 N, how much work is done on the box? • Use the force component that is parallel to the displacement! • m=50.0 kg • d=11.0 m • Theta=35 degrees • Fapplied=90.0 N • W=? • W=Fd • F(x)=?

  9. Example • A 1385 kg car traveling at 61 km/h is brought to a stop while skidding 42 m. What is the work done on the car by frictional forces? • m=1385 kg • vi-=61 km/hr • Vi=17 m/s • Δx=42 m • Vf=0 • W=? • W=Fd • F=? • F=ma

  10. Nonconservative Forces • The work produced by nonconservative forces are dependent on the paths taken • Friction and air resistance are types of nonconservative forces • A conservative force, such as gravity, are not dependent on the path taken

  11. How does an angle impact work? If you have a 10.0 kg object, how much work is done on the object if it is lifted 1 meter straight off the ground? On a ramp that is 30 degrees off the ground (A)? 60 degrees(B)? 1.0m A 10 Kg B 10 Kg

  12. How does an angle impact work? Wf = Ffd Ff = ukFN FN gets larger as the angle gets smaller So… Ff gets smaller, But you still need to Add the Fg So the work Increases with a Higher angle 1.0m A 10 Kg B 10 Kg

  13. Continued • Work against gravity will not change, however! • If they end at the same height the work against gravity will not change • The amount of force needed will change according to the angle, but the distance will change as well to get to the same height • So the work against gravity is the SAME

  14. Work, Energy, and Power Potential Energy

  15. Potential Energy • Energy can either be potential energy or kinetic energy • Potential energy is stored energy • Examples • Chemical • Elastic (bungee cord, trampoline, bow) • Electrical (static charges) • Gravitational potential energy Energy can be converted into different forms by doing work

  16. Gravitational Potential Energy • Due to an object’s position (height) measured relative to a reference point • Gravitational Potential Energy – Ep(or GPE) • Ep=mgh • m=mass • g=9.8 m/s2 • h=height

  17. Example • A 15.0 kg textbook is sitting on a 1.20 m tall table. If the book is lifted 0.80 m above the table, how much gravitational potential energy does it have: • With respect of the table? • With respect to the ground?

  18. Clicker Question • A 1400 kg roller coaster is moved to the top of a track that is 100 m above the lowest part of the track. What is the gravitional potential energy of the coaster? • A) 2000 J • B) 1.4 x 104 • C) 34000 J • D)1.4 x 106 J

  19. Spring/Elastic Potential Energy • The energy available for use in deformed elastic objects • Rubber bands, springs in trampolines, pole-vault poles, muscles • For springs, the distance compressed or stretched = x • Spring constant (k) depends on stiffness of spring, measured in N/m • Force needed to stretch the spring 1 meter

  20. Example • When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table • What is the gravitational potential energy associated with the mass relative to the table? • What is the spring’s elastic potential energy is the spring constant is 400.0 N/m?

  21. Work, Energy and Power Kinetic Energy

  22. Kinetic Energy • Energy of motion • scalar • Ek=1/2 m v2 • Ek= kinetic energy • m=mass • v=speed

  23. Example • A 60.0 kg student is running at a uniform speed of 5.70 m/s. What is the kinetic energy of the student? • Ek=1/2 m v2 • m=60 kg • v=5.70 m/s • Ek=? • Ek=1/2(60)(5.7)2 • Ek=975 J

  24. Clicker Question • The kinetic energy of a 2.1 kg rotten tomato is 1000 J. How fast is it moving? • A) 15.4 m/s • B) 31 m/s • C) 961 m/s • D) 4000 m/s

  25. Work Energy Theorem • If a net force is acting on an objet then the object must be accelerating • The change in kinetic energy is proportional to the net force • ΔEk=Fnetd • d=distance

  26. Example • A sprinter exerts a net force of 260 N over a distance of 35 meters. What is his change in kinetic energy? • ΔEk=Fnetd • Fnet=260 N • d= 35 m • ΔEk=? • ΔEk=260 (35) • ΔEk=9100 J

  27. Example • A student pushes a 25 kg crate which is initially at rest with a force of 160 N over a distance of 15 meters. If there is 75 N of friction, what is the final speed of the crate? • ΔEk=Fnetd • Ek=1/2mv2 • m=25 kg • F applied=160 N • d=15 m • Ff=75 N

  28. Work, Energy, and Power Conservation of Energy

  29. Law of Conservation of Energy • Energy cannot be created or destroyed, only converted into other forms of energy • TOTAL energy is always conserved • Potential energy can be converted to kinetic energy as an object moves • When only conservative forces act on object potential energy is completely converted to kinetic energy • When nonconservative forces like friction act on an object, some energy will be converted to heat

  30. Mechanical Energy • Mechanical Energy is the sum of kinetic energy and all forms of potential energy associated with an object • ME=KE + PE • When only conservative forces act on an object then mechanical energy is conserved

  31. Law of Conservation of Energy (Quantitatively) • Initial Energy= Final Energy • Ei = Ef • GPEi + Kei = GPEf + Kef • mghi + ½ mv2i = mghf + ½ mv2f • GPE=gravitational potential energy

  32. Example • A student falls from the building, if they reach the ground at 5.0 m/s , what height did they fall from? • Vf=5.0 m/s • Hi=? • Vi=0 • Hf=0 • GPEi + KEi= GPEf + KEf

  33. Example • While jumping over The Great Wall of China an 82 kg skateboarder is needs to leave the ramp traveling at 22 m/s.A) How much potential energy is needed to jump over? B) What minimum height should the ramp be? • m=82 kg • Vf=22 m/s • g=9.8 m/s2 • GPE=? • h=? • Ei=Ef • GPEi + KEi= GPEf + KEf • GPEi =Kef • GPE = ½ mv2f

  34. Clicker Question • A 66 kg skateboarder jumps The Great Wall of China, clearly. At the peak of jump he is 18 m high and traveling at 12 m/s . Assuming he started at rest, find his initial height. • A) 10 m • B) 19 m • C) 25 m • D) 30 m

  35. Clicker Question • A 75 kg snowboarder slides up a frictionless rail to a height of 1.75m and slides across it at 2.50 m/s. How much kinetic energy did he have before he went up the rail? • A) 1520 J • B) 1380 J • C) 200 J • D) Impossible to solve

  36. Roller Coasters • Although not perfectly energy efficient, they are a fun way to view how work, gravitational potential and kinetic energy are exchanged

  37. The Downhill skier • When a nonconservative force is applied (friction) the work is negative because it is removing energy from the system What’s this?

  38. Work, Energy, and Power Power

  39. Power • Power (P) is the rate of doing work • Measured in J/s or Watts (W) • Power= Work/time • P=W/t or P=ΔE/t

  40. Clicker Question • Mike performed 5 J of work in 10 seconds. Joe did 3 J of work in 5 seconds. Who produced the greater power? • A) Mike • B) Joe • C) Both produced the same amount of power

  41. Example • Lover’s Leap is a 122 m vertical climb. The record time of 4 min 25 s was achieved by Dan Osman (65 kg). What was his average power output during the climb? • h=122 m • t=4 min 25 s  265 s • m=65 kg • g=9.8 m/s2 • P=? • P=W/t or P= ΔE/t

  42. Example • A 1.00x103 kg car accelerates from rest to a velocity of 15.0 m/s in 4.00 s. Calculate the power output of the car. Ignore friction. • m=1.00 x 103 kg • Vf=15 m/s • t=4.00 s • P=? • P=W/t or P=ΔE/t

  43. Clicker Question • A 68 kg student runs up a flight of stairs 3.2 m high in 4.8 seconds. Determine their power output while running up the stairs. • A) 217.6 W • B) 45.33 W • C) 440 W • D) There is no work in this problem, not enough info

  44. Clicker Question • A 642 kg formula 1 car can reach a speed of 27.78 m/s in 1.7 seconds. What is the power output of the car during this acceleration? • A) 300,000 W • B) 5000 W • C) 150,000 W • D) 3000 W

  45. Another Useful Formula • P=W/t • P=Fd/t • V=d/t • So.. • P=FV • Note this formula is only useful when the velocity is held constant

  46. Example • A student uses 140 N to push a block up a ramp at a constant velocity of 2.2 m/s. What is their power output? • F=140 N • V=2.2 m/s • P=? • P=FV • P=140 (2.2) • P=310 W

  47. Clicker Question • An elevator motor has a power rating of 110 kW. How much force would it exert if it was lifting a load at a constant velocity of 3.0 m/s? • A) 3700 N • B) 37 N • C) 330 N • D) 4 N

  48. Work, Energy, Power Efficiency

  49. Efficiency • A measure of how much of the energy that goes into a machine actually gets used • Machines are useful because they allow us to use less force over a longer distance to do the same work

  50. Efficiency of a Machine • Eff= W out x 100 W in • Eff= P out x 100 P in • There are no units for efficiency because it is a percentage

More Related