Chapter 4, Problem 68GP

a.

To determine

To show: The coefficient of static friction with the ground must be at least ${\mu }_s=\frac{a}{g}$ .

Explanation of Solution

Given Data:

Horizontal acceleration produced by the earth quake is a.

Calculation:

Let the ,ass of the object be m.

The horizontal acceleration is a.

If the coefficient of the static friction be ${\mu }_s$ ,

Hence, the force due to the friction should be equal to the applied external force:

  $\begin{array}{l}{\mu }_{s}mg=ma\\ {\mu }_s=\frac{a}{g}\mathrm{..........}\left(1\right)\end{array}$

b.

To determine

Whether the chair have started to slide on linoleum floor with the coefficient of the static friction 0.25.

Explanation of Solution

Given Data:

The acceleration is 4m/s².

Calculation:

The body will slide if:

  $\frac{a}{g}>{\mu }_s$

As the acceleration experienced is:

  $a=4{\text{m/s}}^2$

Therefore,

  $\begin{array}{l}\frac{a}{g}=\frac{4}{9.8}=0.408\\ \text{whereas,}\\ {\mu }_s=0.25\\ \text{Hence,}\\ \frac{a}{g}>{\mu }_s\end{array}$

Thus, the body will slide.