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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

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Physics of the ESD Lower School Playground

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  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

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