Question

As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

Answer 1

Mass of the albertine =60kg
Compressed length of the string (\(\displaystyle\triangle{x}\))=5.0
Acceleration due to gravity \((g)=9.8m/s^2\)
From the principle of law of conservation of energy,
\(\displaystyle{\frac{{{1}}}{{{2}}}}{k}\triangle{x}^{{2}}=\mu_{{k}}{m}{g}\triangle{s}\)
\(\displaystyle\mu_{{k}}={\frac{{{k}\triangle{x}^{{2}}}}{{{2}{m}{g}\triangle{s}}}}\)
\(\displaystyle={\frac{{{95.0}\ \frac{{N}}{{m}}{\left({5.0}\ {m}\right)}^{{2}}}}{{{2}{\left({60.0}\ {k}{g}\right)}{\left({9.8}\ \frac{{m}}{{s}^{{2}}}\right)}{\left({19.8}\ {m}\right)}}}}\)
\(\displaystyle={0.102}\)