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# Physics of the ESD Lower School Playground - PowerPoint PPT Presentation

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

Grant Fitts

• 1 rev = 2.6 seconds (at max velocity)

• 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

• 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 going

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?

• 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 efficiency

• 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

velocities

• 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

• 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.

• ∆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 acceleration

1.69 = u(g)cosø

1.69 = u(9.8)cos16.6

µ = .18

The difference is friction

• 35 steps

-each .18 meters down

1.4 seconds to fall total height

• Depth = 35(.18)

• = 6.3meters down

• Vf2 = 2a∆x

• V = √(2(9.8)(6.3))

• V = 11.11m/s for a falling ball

• 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

• 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

• 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.

• 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 velocities

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