Chapter 4, Problem 25P

* You want to determine the coefficient of kinetic friction between a $\text{1 m }\times \text{ 1 m}$ rug and a wooden floor. You obtain a piece of the same rug of size $\text{10 cm }\times \text{ 10 cm}$

(which has a surface area 100 times smaller than the entire rug), a scale for measuring mass, a force meter, and an object of mass $m_{\text{o}}$. Which of the following procedures would you choose to obtain the correct value of kinetic friction between the rug and the floor?

a. Put the object on the piece of rug. Measure the force $F_{\text{H on RP}}$ exerted by the hand on the rug piece in the horizontal direction while moving it with constant speed along the wooden floor. Calculate the coefficient of kinetic friction as $\mu \text{k=}\frac{F_{\text{H on RP}}}{m_{\text{o}}g}$.

b. Use the same method described in (a) but calculate the coefficient of friction as $\mu \text{k=}\frac{100·F_{\text{H on RP}}}{m_{\text{o}}g}$.

c. Use the same method described in (a) but also measure the mass of the rug piece $m_{\text{RP}}$ and calculate the coefficient of friction as $\begin{array}{l}\mu \text{k=}\frac{F_{\text{H on RP}}}{(m_{\text{o}}+m_{\text{RP}})g}\\ \end{array}$.

d. Use the same method described in (c) but calculate the coefficient of friction as $\mu \text{k=}\frac{100·F_{\text{H on RP}}}{(m_{\text{o}}+m_{\text{RP}})g}$.