Solution Found!
A typical value for the coefficient of quadratic air
Chapter 2, Problem 2.26(choose chapter or problem)
A typical value for the coefficient of quadratic air resistance on a cyclist is around \(c=0.20 \mathrm{~N} /(\mathrm{m} / \mathrm{s})^{2}\). Assuming that the total mass (cyclist plus cycle) is \(m=80 \mathrm{~kg}\) and that at \(t=0\) the cyclist has initial speed \(v_{\mathrm{o}}=20 \mathrm{~m} / \mathrm{s}\) (about 45 mi/h) and starts to a coast to stop under the influence of air resistance, find the characteristic time \(\tau=m / c v_{\mathrm{o}}\). How long will it take him to slow to 15m/s. What about 10 m/s? And 5 m/s (below about 5 m/s, it is certainly not reasonable to ignore friction, so there is no point persuing this calculation to lower speeds)
Questions & Answers
(2 Reviews)
QUESTION:
A typical value for the coefficient of quadratic air resistance on a cyclist is around \(c=0.20 \mathrm{~N} /(\mathrm{m} / \mathrm{s})^{2}\). Assuming that the total mass (cyclist plus cycle) is \(m=80 \mathrm{~kg}\) and that at \(t=0\) the cyclist has initial speed \(v_{\mathrm{o}}=20 \mathrm{~m} / \mathrm{s}\) (about 45 mi/h) and starts to a coast to stop under the influence of air resistance, find the characteristic time \(\tau=m / c v_{\mathrm{o}}\). How long will it take him to slow to 15m/s. What about 10 m/s? And 5 m/s (below about 5 m/s, it is certainly not reasonable to ignore friction, so there is no point persuing this calculation to lower speeds)
ANSWER:Step 1 of 3
The characteristics time is given by,
\(r=\frac{m}{c v_{0}}\)
Here \(m\) is the mass, \(c\) is the coefficient of the quadratic resistance coefficient on the cyclist, \(v_{0}\) is the initial speed.
Substitute 80 kg for \(m\), \(0.20 \mathrm{~N} /(\mathrm{m} / \mathrm{s})^{2}\) for \(c\) , \(20 \mathrm{~m} / \mathrm{s}\) for \(v_{0}\) in the above equation.
\(\begin{array}{c} I=\frac{80}{0.2(20)} \\ I=20 \mathrm{~s} \end{array}\)
Reviews
Review this written solution for 101069) viewed: 369 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 2 - Problem 2.26
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 101069) viewed: 369 isbn: 9781891389221 | Classical Mechanics - 0 Edition - Chapter 2 - Problem 2.26
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