- #1
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Homework Statement
From http://library.thinkquest.org/10796/index.html (#6)
A book has a mass of 400 g. When you slided the book against the floor with 5 N, it accelerated at the rate of -1.5 m/s2. What would the coefficient of friction between the book and the floor be?
[tex]g=9.80m/s^2[/tex]
Homework Equations
[tex]F=ma[/tex]
[tex]F_f=\mu F_N[/tex]
[tex]F_N=mg[/tex] (The site actually states the normal force to be equal to negative mass times gravitational acceleration, but with a negative value for gravitational acceleration. I'm going with Wikipedia, though.)
[tex]n\textrm{g}=\frac{n}{1000}\textrm{kg}[/tex]
The Attempt at a Solution
First off, I'd like to say that this site was made by high school seniors, so I'm put in the uncomfortable position of not being able to readily accept everything that's there.
Next, why is the applied force positive but the acceleration negative? I'll just assume that that was a mistake and that the applied force should actually be -5N.
[tex]-5\textrm{N}+F_f=F\implies F_f=F+5\textrm{N}[/tex]
(Right? It seems right to me...)
[tex]F=0.4\textrm{kg} \times -1.5\textrm{m/s}^2[/tex]
[tex]F_f=\mu \times 0.4\textrm{kg} \times 9.80 \textrm{m/s}^2[/tex]
[tex]\mu=\frac{F_f}{0.4\textrm{kg} \times 9.80 \textrm{m/s}^2}=\frac{0.4\textrm{kg}\times -1.5\textrm{m/s}^2+5\textrm{N}}{0.4\textrm{kg} \times 9.80 \textrm{m/s}^2}[/tex]
[tex]\mu=1.122[/tex]
I get the same answer when I keep the applied force positive, make the acceleration positive, and use [tex]5\textrm{N}-F_f=F\implies F_f=5\textrm{N}-F.[/tex]
Yet, the site's answer is 0.15.
I even tried using a positive applied force with a negative acceleration (pretending that friction could make an object go in the opposite direction of the applied force).
[tex]5\textrm{N}-F_f=F\implies F_f=5\textrm{N}-F[/tex]
[tex]F=0.4\textrm{kg} \times -1.5\textrm{m/s}^2[/tex]
[tex]F_f=\mu \times 0.4\textrm{kg} \times 9.80 \textrm{m/s}^2[/tex]
[tex]\mu=\frac{F_f}{0.4\textrm{kg} \times 9.80 \textrm{m/s}^2}=\frac{5\textrm{N}-0.4\textrm{kg}\times -1.5\textrm{m/s}^2}{0.4\textrm{kg} \times 9.80 \textrm{m/s}^2}[/tex]
[tex]\mu=1.429[/tex]
Then I realized that, using 400 instead of 0.4, you get -0.152, -0.152, and 0.154, respectively, for the three attempts described above.
Somebody, please, what is going on here?? I'd really appreciate some help, and it'd be great if you simply told me that the site was really wrong. :tongue:
Thank you!