MODEL 2 The mscript used for the is mec_fr_mg_bv2.m Analytical Approach For the vertical motion of an object through a fluid, the forces acting on the object are the gravitational force (weight) and the resistive force In our FG FR. frame of reference, down is the positive direction. The equation of motion of the object is determined from Newton’s Second Law. is the acceleration of the object at any instance. a The initial conditions are When = 0, the velocity is constant = where is the terminal velocity a v vT vT We start with the equation of motion then integrate this equation where the limits of the integration are determined by the initial conditions and (t = 0 = v and final conditions and (t v0) v). Since the acceleration depends upon its a more difficult problem then for the v2 linear resistive force example. We have to do separate analytical calculations for the motion when the object is falling or rising. Velocity of the object is always positive (falling object) Equation of motion valid only if
MODEL 2 The mscript used for the is mec_fr_mg_bv2.m Analytical Approach For the vertical motion of an object through a fluid, the forces acting on the object are the gravitational force FG (weight) and the resistive force FR. In our frame of reference, down is the positive direction. The equation of motion of the object is determined from Newton’s Second Law. a is the acceleration of the object at any instance. The initial conditions are When a = 0, the velocity is constant v = vT where vT is the terminal velocity We start with the equation of motion then integrate this equation where the limits of the integration are determined by the initial conditions (t = 0 and v = v0) and final conditions (t and v). Since the acceleration depends upon v2 its a more difficult problem then for the linear resistive force example. We have to do separate analytical calculations for the motion when the object is falling or rising. Velocity of the object is always positive (falling object) Equation of motion valid only if