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Terminal Velocity, Weight & Area As v increases, so does air friction… …until F = W-f =0. Now a=0, and the maximum or “terminal” velocity is achieved Curveballs Lab: Coffee Filter, Air Drag & Terminal Velocity with Motion Detector Ailerons Motion in the presence of resistive forces Motion in viscous media. Objects interact with the medium through which they are moving. - Air - Water, oil, liquids. The resistive forces depend on the speed of the object. F ~ v: Objects falling in liquid, tiny objects falling in air. F ~ v2: Large objects moving in air. Terminal velocity. When the resistive force of the falling object is equal to the gravitational force on the object. Examples: - skydivers - soap bubbles falling in air - small spheres dropping in liquid. Air drag at high speeds. For objects moving at high speeds through air: Resistive force: 1 2 R D Av 2 Where: D… Drag coefficient of object (depends on shape) …density of air A… cross-sectional area of object v… velocity of object Example CC Sabathia fires a baseball (m = 0.145 kg) past you at 100 miles/hr (45 m/s). (a) Calculate the resistive force acting on the ball at that speed. D… Drag coefficient = 0.284 …density of air = 1.29 kg/m3 r… radius of baseball = 0.037 m v… velocity of object Air Drag a.k.a. Fluid Drag Fluid friction = ½ CAv2 @ V terminal, F = W – f = 0 Solve for v: mg - ½ CAv2 = 0 V terminal = (2mg/ CA)½ Drag Forces ©2008 by W.H. Freeman and Company What factors influence drag? • Shape of the object. – Cars and planes are given aerodynamic shape to reduce drag. • Properties of the fluid. – Denser fluids increase drag. • Speed of the object relative to the fluid. Fd bv n n 1 at low speeds. n 2 at higher speeds. Terminal Velocity • Because the drag force increases with increasing velocity, an object in free fall will reach a speed where the drag force balances the force of gravity. • This speed is called terminal velocity. Terminal Velocity Fd mg ma y • bv mg ma y n • At terminal velocity bvTn mg 0 mg v b n T mg vT b 1 n Getting to Terminal Velocity • Because the drag force depends on velocity, at first the drag force is small and the motion is like free fall. • At terminal velocity the velocity is constant. • The graph is exponential growth. v A(1 e Bt ) Getting to Terminal Velocity Fd mg ma y bv mg may n • Assume n 1. dv bv mg m dt dv b vg dt m v A(1 e Bt ) v vT 1 e g t vT