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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 - PowerPoint PPT Presentation
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Physics of the ESD Lower School
Playground
Physics of the ESD Lower School
Playground
Grant FittsGrant Fitts
Spin WheelSpin Wheel
Radius = 1.17 m 1 rev = 2.6 seconds (at
max velocity)
Radius = 1.17 m 1 rev = 2.6 seconds (at
max velocity)
Just to hold on…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
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
Spiral SlideSpiral Slide
Height = 1.77 mStraight for .9 mFalls .46 m to
groundBall travels 1.3 m
during fall
Height = 1.77 mStraight for .9 mFalls .46 m to
groundBall travels 1.3 m
during fall
How fast it should be going
How fast it should be going
(.5) mv2 = mghV = √(2gh)
= √(2 x 9.8 x 1.77)
V = 5.89 m/s
theoretical
(.5) mv2 = mghV = √(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 =.306V = 1.3 / .306V = 4.24 m/s
.46 = .5 (a) t2
.46 = .5 (9.8)t2
T2 = √(.46/ (9.8 x .5 ))T =.306V = 1.3 / .306V = 4.24 m/s
Why the difference?Why the difference?
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 - 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%
4.24 -5.89 / 5.89 x 100 = %error
= 28.01 % 4.24 / 5.89 = eff. Efficiency=
71.98%
Straight Bar Hold 4.35 meters long-.96 seconds to travel 2.6 before-hand-ran in .4 seconds
Velocity and efficiency 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 = 2.562.56 / 6.5 = effic.Efficiency = 39.4%
Racing SlideRacing Slide
• Height = 1.2 m• Falls .4 m• Travels 1 m in fall
• Height = 1.2 m• Falls .4 m• Travels 1 m in fall
velocitiesvelocities• .5 (mv2) = mgh• .5v2 = 9.8(1.2)• V = 4.85 m/s• Theoretical------------------------------.4 = .5(9.8)t2
T = .286 seconds1 = .286vV = 3.497 m/sactual
• .5 (mv2) = mgh• .5v2 = 9.8(1.2)• V = 4.85 m/s• Theoretical------------------------------.4 = .5(9.8)t2
T = .286 seconds1 = .286vV = 3.497 m/sactual
• 3.497 - 4.85 / 4.85 x 100 = %error
• 27.9 % error
• 3.497 - 4.85 / 4.85 x 100 = %error
• 27.9 % error
Swing!Swing!
Radius = 1.86 m Radius = 1.86 m
To Go in a Circle…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
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
Pendulum statusPendulum 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.
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.
Hand RailHand Rail
∆h = .7 m Length = 2.45 m 2.1 seconds to slide
∆h = .7 m Length = 2.45 m 2.1 seconds to slide
Angles and accelerationAngles and acceleration
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.
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
sin-1(.7 / 2.45) = ø Ø=16.6 degrees gsinø = gx
2.45 = .5(2.8) t2
T = 1.322 seconds
The difference is frictionThe difference is friction
1.11(m) = 2.8(m) -uNcosø
1.69 = u(g)cosø 1.69 = u(9.8)cos16.6 µ = .18
1.11(m) = 2.8(m) -uNcosø
1.69 = u(g)cosø 1.69 = u(9.8)cos16.6 µ = .18
Big Stairs to Gym
35 steps
-each .18 meters down
1.4 seconds to fall total height
How far downHow far down
Depth = 35(.18) = 6.3meters down Vf
2 = 2a∆x
V = √(2(9.8)(6.3)) V = 11.11m/s for a falling ball
Depth = 35(.18) = 6.3meters down Vf
2 = 2a∆x
V = √(2(9.8)(6.3)) V = 11.11m/s for a falling ball
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
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
The HillThe 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
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
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.
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Mothers’ Day Out SlideMothers’ Day Out Slide
H = 2.17 m Time = 3.2
seconds Track length = 4
m
H = 2.17 m Time = 3.2
seconds Track length = 4
m
Differences in velocitiesDifferences in velocities
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
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
2.498 - 6.52 / 6.52 x 100 = %error
61.69% error
sourcessources
http://cielovistahoa.com/images/playground.jpg
http://cielovistahoa.com/images/playground.jpg