A $10-$kg block slides down a smooth inclined surface $($ $=20$o$)$ as shown

in the following figure. Assume the velocity distribution in the $0\mathrm{.}1-$mm gap is linear,

and the area of the block in contact with the oil is A $=0\mathrm{.}1$ m$2.$

Determine the terminal velocity of the block if the $0\mathrm{.}1-$mm gap between the block and

the surface contains SAE $30$ oil at $15\mathrm{.}6$ oC $($see Table $1\mathrm{.}6).$

$5.[10$ points$]$ Some measurements on a blood sample at $37$ oC indicate a shearing stress

of $0\mathrm{.}52$ N$/$m$2$ for a corresponding shearing strain rate of $200$ s$1,$ while the measured

value of shearing stress is $0\mathrm{.}01$ N$/$m$2$ at a smaller shearing strain rate of $0\mathrm{.}1$ s$1.$

Determine the apparent viscosities of the blood at the two different rates of shearing

strain, and compare them with the viscosity of water at the same temperature $($Hint:

see Table B$\mathrm{.}2,$ do interpolation between temperatures to get the value at $37$ oC$).$

Make a conclusion about the type of non$-$Newtonian behavior of the blood sample.

$2$ Problem $5-49$

Cantilevered rod $\backslash ($ O A $\backslash )$ is $0\mathrm{.}5$ m long, and made from AISI $1010$ hot$-$rolled steel. A constant force and torque are applied as shown. Determine the minimum diameter, $\backslash ($ d $\backslash ),$ for the rod that will achieve a minimum static factor of safety of $2$

$($a$)$ using the maximum$-$shear$-$stress failure theory.

$($b$)$ using the distortion$-$energy failure theory.