1 / 24

Physics of the ESD Lower School Playground

Physics of the ESD Lower School Playground. Grant Fitts. Spin Wheel. Radius = 1.17 m 1 rev = 2.6 seconds (at max velocity). Just to hold on…. V = 2(1.17) π / 2.6 V t =2.83 m/s Mv 2 /r = F 81.81(2.83 2 )/1.17 = F F = 560 Newtons. Spiral Slide. Height = 1.77 m Straight for .9 m

ajaxe
Télécharger la présentation

Physics of the ESD Lower School Playground

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. Physics of the ESD Lower School Playground Grant Fitts

  2. Spin Wheel • Radius = 1.17 m • 1 rev = 2.6 seconds (at max velocity)

  3. Just to hold on… • V = 2(1.17)π / 2.6 • Vt =2.83 m/s • Mv2/r = F • 81.81(2.832)/1.17 = F • F = 560 Newtons

  4. Spiral Slide • Height = 1.77 m • Straight for .9 m • Falls .46 m to ground • Ball travels 1.3 m during fall

  5. (.5) mv2 = mgh V = √(2gh) = √(2 x 9.8 x 1.77) V = 5.89 m/s theoretical .46 = .5 (a) t2 .46 = .5 (9.8)t2 T2 = √(.46/ (9.8 x .5 )) T =.306 V = 1.3 / .306 V = 4.24 m/s How fast it should be going

  6. 4.24 = 5.89 - 2a∆x 4.24 = 5.89 -2a(.9) A =.917 m/s2 Ff = uN .917(m) = uN U =(.145)(9.8)/.917 µ= 1.55 4.24 -5.89 / 5.89 x 100 = %error = 28.01 % 4.24 / 5.89 = eff. Efficiency= 71.98% Why the difference?

  7. Straight Bar Hold • 4.35 meters long -.96 seconds to travel • 2.6 before-hand -ran in .4 seconds

  8. 2.6 /.4 = Vi Vi = 6.5 m/s 4.35/ .96 = Vf Vf (average) = 4.53 4.53 = 6.5 - 2a(2.175) A = -.453 m/s2 81.81(.453) = u(801.74) µ = .046 Velocity retained (%) Vf = 6.5 - 2 (.453)(4.35) Vf = 2.56 2.56 / 6.5 = effic. Efficiency = 39.4% Velocity and efficiency

  9. Racing Slide • Height = 1.2 m • Falls .4 m • Travels 1 m in fall

  10. .5 (mv2) = mgh .5v2 = 9.8(1.2) V = 4.85 m/s Theoretical ------------------------------ .4 = .5(9.8)t2 T = .286 seconds 1 = .286v V = 3.497 m/s actual 3.497 - 4.85 / 4.85 x 100 = %error 27.9 % error velocities

  11. Swing! • Radius = 1.86 m

  12. To Go in a Circle… • R = 1.86 m • Mg = mv2/r • 9.8 = v2/1.86 • Vf = 4.27 m/s • .5m(4.272 - vi2) =-mgh • .5(18.23 - vi2) = -9.8(3.72) • Vi = 9.55 m/s running start

  13. Pendulum status • Times of full swing (from start) in seconds 2.5, 2.7, 2.8, 2.7, 2.8,2.8,2.9,2.9,3.0,3.1 Not quite a pendulum because the chain will lose tension when the swing breaches 90 degrees and then drops straight down, jerking forward and losing angular velocity.

  14. Hand Rail • ∆h = .7 m • Length = 2.45 m • 2.1 seconds to slide

  15. 2.45 = .5(a)t2 T = 2.1 2.45 = .5a(2.12) A = 1.11 m/s2 1.11 = 9.8sinø Ø = 6.5 degrees. sin-1(.7 / 2.45) = ø Ø=16.6 degrees gsinø = gx 2.45 = .5(2.8) t2 T = 1.322 seconds Angles and acceleration

  16. 1.11(m) = 2.8(m) -uNcosø 1.69 = u(g)cosø 1.69 = u(9.8)cos16.6 µ = .18 The difference is friction

  17. Big Stairs to Gym • 35 steps -each .18 meters down 1.4 seconds to fall total height

  18. How far down • Depth = 35(.18) • = 6.3meters down • Vf2 = 2a∆x • V = √(2(9.8)(6.3)) • V = 11.11m/s for a falling ball

  19. Tricycle Racing Hill • Straight section at bottom = 3.52 m • Time after pedaling down hill = 1.9 seconds • Time on section without pedaling = 1.1 seconds • Hill = 14.75 meters

  20. The Hill • 3.52 / 1.1 = 3.2 m/s • 3.22 = 2a∆x • 3.22 = 2a(14.75) • A= .347 m/s2 • Gsinø - ugcosø = .347 • 9.8sinø -(.4)(9.8)cosø= .347 • Ø = 23.68 degrees • Sin23.68= h/ 14.75 • H = 5.9 m .5v2 = 9.8(5.9) V = 10.75 3.2 - 10.75 / 10.75 x 100 = %error 70.2% error

  21. Racing tip… • 3.52 / 1.9 = 1.85 m/s • 1.852 = 2a(14.75) • A = .116 • 3.2(x) = 1.85 • X = .578 • Attempting to pedal cuts your speed to 57.8% of what it would be. • http://www.facebook.com/profile.php?id=533654442&ref=profile

  22. Mothers’ Day Out Slide • H = 2.17 m • Time = 3.2 seconds • Track length = 4 m

  23. gh = .5v2 9.8(2.17) = .5v2 V = 6.52 (theoretical) 4 = .5a(3.22) A = .78 m/s2 Vf2 = 2(.78)4 Vf = 2.498 m/s 2.498 - 6.52 / 6.52 x 100 = %error 61.69% error Differences in velocities

  24. sources • http://cielovistahoa.com/images/playground.jpg

More Related