Question

Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for drag using Ca for known values of drag coefficients. Here a 1 for where 7. drag the formula F, viscous fluid. a very drag Problem 36 (Small Reynolds Number - [Module 1: SLO 1]). In the case of small Reynolds number (Re 1), the drag force on an object moving through by Fdrag, is known to be dircctly proportional to the speed of the object relative to the fluid: fluid, denoted Fdrag kv where k is a dimensional constant of proportionality. Assume that a released from rest at the origin and take the y-axis pointing downward in the direction of motion with the origin at the initial position. In this problem you will be asked to derive formula for the equation governing the motion of the object and solve this equation to answer the following questions. Be sure to verify that your formula is dimensional consistent tiny particle is a 1 pt] (a) Draw a free-body diagram for this situation and use your free-body diagram with Newton's second law to write down the governing equation for this situation 1 pt (b) Derive 1 pt (c) Integrate the expression for v v(t) to find the position of the particle function of time y y(t) 1 ptl (d) Determine the speed of the terminal velocity vterm [1 pt] (e) Express the large t behavior of the position function y = y(t) in terms of verm function of time v = v(t) an expression for the velocity as a as a

Answer 1

Pre body diagesn Fdeay fmii dv -rtm - - e guit ulta 1K, c) K2 For terminal reloat, to + Viem t ea