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Exploring the Physics of Rock Climbing and Sky Diving - Nathan Williamson -

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Kinematics Concepts Acceleration is a derivative of Velocity Velocity is a derivative of Position Terminal Velocity Acceleration x Time Drag Coefficient

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Rock Climbing

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Skydiving - Reaching Terminal Velocity The SLOPE is the Velocity 65.2 m/s = 148 mph

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Parachute Deployment - Velocity Change The AREA = a dt = v Max Acc = 3.7 g’s! Somersaults Final Chute Velocity

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Velocity Change From Parachute (14.4g x sec) – (8.3g x sec) = 6.1g x sec v = (6.1g x sec) x 9.8m/s/s = 59.78m/s Subtract Velocity Change from Terminal Velocity 65.2m/s - 59.78m/s = 5.42m/s New Velocity (12 mph) Most of the Terminal Velocity lost when chute deployed Area below 1 gTotal Area vv

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Drag Coefficient Force of Drag: F D = -bv 2 where b is the drag coefficient As velocity increases, the magnitude of the resistive force approaches the gravitational force: mg – bv 2 = 0 Therefore, terminal velocity: v T = (mg / b) 1/2 Giving average drag coefficient of: b = mg / v T 2 b = 160kg x 9.8m/s/s / (65.2m/s) 2 = 0.369 (Total Mass)

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Drag Coefficient Typical Drag Coefficients: Single Skydiver – 1.0-1.4 Bicyclist – 0.9 Hummer H2 – 0.57 Ferrari Testarossa – 0.36 Smooth Sphere – 0.1 Learjet 24 – 0.022

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