Drag Variables

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I need you to solve those two problems i have attached. please, show me all the work step by step. I prefer to be hand written. this is the book that we are using https://www.qom.ac.ir/Portal/File/ShowFile.aspx?ID...

if you need anything just ask me. DO NOT SKIP ANY PART.

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4. JRT 2.14. Separation of variables for an exponential drag force. [10 pts.] Use the method of separation of variables (see JRT Problem 2.7) to solve the following: A mass m is constrained to move along the x axis subject to a force F(v) = -Foe", where Fo and V are constants. (a) Find the time-dependent speed (t), if the initial velocity is vo > 0 at t = 0. (b) At what time does the mass come instantaneously to rest? (c) Integrate v(t) to obtain x(t). (d) Determine the distance the mass travels before coming instantaneously to rest 5. Automobile with quadratic air resistance. [10 pts.] Consider an automobile moving through the air (around STP) at typical to maximum driving speeds. (a) Using some suitable estimates, demonstrate that quadratic air resistance dominates by estimating the Reynold's number for the automobile. Yes, you may assume a spherical car for this approximation – in what follows we will use more realistic estimates of the drag coefficient, cross-sectional area, etc. (b) Several years ago the Bugatti Veyron Super Sport claimed the Guinness Book of Records title for the fastest production car: achieving a top speed of approximately 260 mph resulting from a whopping 1000 bhp. Note: bhp refers to "brake horsepower" meaning horsepower produced at the engine output only, not necessarily that provided at the wheels, which is naturally lower due to friction in the gearbox, differential, driveshafts, etc. Nevertheless, use this power output (assume that it is consumed entirely in fighting the force of air drag, i.e., ignore rolling resistance and other forms of friction) to determine the "terminal velocity" (or top speed) of the Veyron in mph. Take the drag coefficient to be k = 0.36 and the frontal cross-sectional area to be 2.07 m2. Hint: relate instantaneous power to force and velocity. (c) Compare your answer in (b) to the recorded top speed of the Bugatti Veyron. Note: My calculation resulted in a top speed shy of the measurement, which seems odd given that I expected to overestimate the actual value. Briefly explain why I might have thought this. Perhaps the error arises from a difference in cross-sectional area or drag coefficient - Engineers often report the "drag area" which is the product k A. Note: the Veyron lowers the suspension automatically at high speed which reduces the drag area. How much would it need to reduce to explain the difference? What else might account for the discrepancy? (d) Repeat part (b) for a car of your choice (other than the Bugatti Veyron), perhaps your daily driver or "aspirational car". You will need numbers and/or reasonable estimates for the drag coefficient, cross-sectional area, and top speed. Wikipedia has a nice table of automobile drag coefficients (Engineers often use ce for what JRT calls k) and cross-sectional areas for a number of different automobile manufacturers and models.
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