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Physics of the ESD Lower School PlaygroundPowerPoint Presentation

Physics of the ESD Lower School Playground

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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
- Vt =2.83 m/s
- Mv2/r = F
- 81.81(2.832)/1.17 = F
- F = 560 Newtons

Spiral Slide

- Height = 1.77 m
- Straight for .9 m
- Falls .46 m to ground
- Ball travels 1.3 m during fall

(.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 going4.24 = 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?Straight Bar Hold

- 4.35 meters long
-.96 seconds to travel

- 2.6 before-hand
-ran in .4 seconds

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 efficiencyRacing Slide

- Height = 1.2 m
- Falls .4 m
- Travels 1 m in fall

.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

velocitiesSwing!

- Radius = 1.86 m

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

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.

Hand Rail

- ∆h = .7 m
- Length = 2.45 m
- 2.1 seconds to slide

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 accelerationBig Stairs to Gym

- 35 steps
-each .18 meters down

1.4 seconds to fall total height

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

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

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

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 Slide

- H = 2.17 m
- Time = 3.2 seconds
- Track length = 4 m

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 velocitiessources

- http://cielovistahoa.com/images/playground.jpg

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