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Physics 1 Problem Solutions 78

Physics 1 Problem Solutions 78 - 74 Chapt 6 Newtons Laws...

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74 Chapt. 6 Newton’s Laws and Dynamics II c) The second law with the forces written explicitly is a differential equation for velocity as function of variable time. A differential equation being an equation for a function that contains derivatives of various orders of the function. To solve a differential equation is to find the function as an explicit function of the variable. Many, many physical problems come down to solving differential equations. In this case, verify that v = v 0 e Ct + F loco Cm (1 e Ct ) is the explicit solution of the differential equation: v 0 is an initial velocity at time zero. What is the differential equation and solution if F loco = 0? 006 qfull 00740 3 3 0 tough math: quadratic drag force 12. The quadratic drag force magnitude on a body is F drag = bv 2 = 1 2 CρAv 2 , where C is the dimensionless drag coefficient (which is typically in the range 0.4 to 1 [HRW-104] and is set by all kinds of things like shape and texture of the body), ρ is fluid density, A is the area of body perpendicular to the flow (i.e., the cross sectional area), and
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