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

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