Chapter 8.8, Problem 107P

To determine

The smallest required coefficient of static friction.

Answer to Problem 107P

The smallest required coefficient of static friction $\left({\mu }_s\right)$ is $\underset{\_}{0.145}$.

Explanation of Solution

Given:

The thrust (P) is 800 lb.

The torque (M) is $15\text{lb}\cdot \text{ft}$.

The distance between the mid-point of the annular ring to starting of the bearing $\left(R_1\right)$ is 1 in.

The distance between the mid-point of the annular ring to ending of the bearing $\left(R_2\right)$ is 2 in.

Determine the smallest required coefficient of static friction $\left({\mu }_s\right)$ by using the relation.

$M=\frac{2}{3}{\mu }_{s}P\left(\frac{R_2^3-R_1^3}{R_2^2-R_1^2}\right)$ (I)

Conclusion:

Substitute $15\text{lb}\cdot \text{ft}$ for M, 800 lb for P, 1 in. for $R_1$, and 2 in. for $R_2$ in Equation (I).

$\begin{array}{l}\left(15\text{lb}\cdot \text{ft}\times \frac{\text{12}\text{in}\text{.}}{\text{1}\text{ft}}\right)\text{lb}\cdot \text{in}\text{.}=\frac{2}{3}{\mu }_s\times 800\times \left(\frac{2^3-1^3}{2^2-1^2}\right)\\ 180=1,244.44{\mu }_s\\ {\mu }_s=\frac{180}{1,244.44}\\ {\mu }_s=0.145\end{array}$

Thus, the smallest required coefficient of static friction $\left({\mu }_s\right)$ is $\underset{\_}{0.145}$.