Solution Found!
A mass m has velocity vo at time t = 0 and coasts along
Chapter 2, Problem 2.8(choose chapter or problem)
A mass m has velocity \(v_{0}\) at time \(t=0\) and coasts along the x axis in a medium where the drag force is \(F(v)=-c v^{3 / 2}\). Use the method of Problem 2.7 to find v in terms of the time t and the other given parameters. At what time (if any) will it come to rest?
Questions & Answers
(2 Reviews)
QUESTION:
A mass m has velocity \(v_{0}\) at time \(t=0\) and coasts along the x axis in a medium where the drag force is \(F(v)=-c v^{3 / 2}\). Use the method of Problem 2.7 to find v in terms of the time t and the other given parameters. At what time (if any) will it come to rest?
ANSWER:Step 1 of 2
It is given that the initial velocity of the mass at \(t=0\) is \(v_{0}\).
Let the velocity after time t be v.
The drag force is given by,
\(F(v)=-c v^{\frac{3}{2}}\)
But, \(F(v)=m \frac{d v}{d t}\), therefore,
\(\begin{aligned} m \frac{d v}{d t} & =-c v^{\frac{3}{2}} \\ \frac{d v}{v^{\frac{3}{2}}} & =-\frac{c}{m} d t \end{aligned}\)
Reviews
Review this written solution for 100979) viewed: 690 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 2 - Problem 2.8
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students
Review this written solution for 100979) viewed: 690 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 2 - Problem 2.8
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students