4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.
4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of time. Assume that air resistance is proportional to the instantaneous velocity, with a constant of proportionality k > 0 (this is called the drag coefficient). Take the downward direction to be positive. (b) Solve the differential equation subject to the initial condition v(t = 0) = vo. (c) Determine the terminal velocity of the mass.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.33P
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![4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of
time. Assume that air resistance is proportional to the instantaneous velocity, with a
constant of proportionality k > 0 (this is called the drag coefficient). Take the downward
direction to be positive.
(b) Solve the differential equation subject to the initial condition v(t = 0) = vo.
(c) Determine the terminal velocity of the mass.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b020904-503e-46f0-a83a-8c74ba785f01%2F8da52894-3981-4f4d-b8d9-38984812c118%2F5ot236q_processed.png&w=3840&q=75)
Transcribed Image Text:4. (a) Find a differential equation to model the velocity v of a falling mass m as a function of
time. Assume that air resistance is proportional to the instantaneous velocity, with a
constant of proportionality k > 0 (this is called the drag coefficient). Take the downward
direction to be positive.
(b) Solve the differential equation subject to the initial condition v(t = 0) = vo.
(c) Determine the terminal velocity of the mass.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given, mass of the object = m.
Let 'v' be the instantaneous velocity of the object free falling.
Air resistance is assumed proportional to instantaneous velocity as: ; where is the proportionality constant.
(a) Free body diagram of the falling mass is drawn below.
Here, ; where acceleration of the mass,
------------------------------ (1)
Equation (1) represents the differential equation to model velocity (v) of falling mass (m).
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