Wednesday, October 31, 2012

Water Slide Collisions!

Water Slide Collisions

Nitro Racer – Water Country USA Williamsburg, Virginia

Vertical Drop:  150ft (45.7m)
Length of Slide 320ft (97.5m)

Mass of Kid:  40kg
Mass of Father:  80kg
Collision occurs over .05s

Potential Energy = mgh
Kinetic Energy = 1/2mv2

Kid drops to vertical elevation of 25ft (7.6m)
Kid PE = (40kg)(9.8m/s2)(7.6) = 2980J

Man Drops to vertical elevation of 25ft (7.6m) before collision

Man PE at 95.5m = (80kg)(9.8m/s2)(45.7) = 35800J
Man PE at 7.6m = (80kg)(9.8m/s2)(7.6) = 5960J

Man KE at 7.6m = -mgh + mgh - mmg * sin(q)(d) =  Velocity of man before collision = -(80kg * 9.8m/s 2 * 7.6m) + (80kg * 9.8m/s2 * 45.7m) – (.2 *80kg*  9.8m/s2)(sin 28)(97.5m-16.2m) = 24.4m/s

The Collision!
M1V1 + M2V2 = v(M1+M2)
(80kg)(24.4m/s) + (40kg)(0m/s) = (120kg)(v) v= 16.2 m/s

Impulse = m∆v
Impulse = 120kg(16.2m/s-24.4m/s) = -984kg*m/s
Force = Impulse / ∆t
Force = 984kg*m/s / .05s

19,700N Very possible that serious injuries were sustained
30,000N needed to break some bones such as the patella

Chances are that the bones would not break!