Current Attempt in Progress

An automobile engine supplies power, $\backslash ($ P$=230\backslash$mathrm$\{$hp$\}\backslash ),$ at a rotational speed of $3900$ rpm to a driveshaft. If the allowable shear stress in the driveshaft must be limited to $\backslash (\backslash$tau$\_\{\backslash$text $\{$allow $\}\}=4\mathrm{.}75\backslash$mathrm$\{$ksi$\}\backslash ),$ determine:

$($a$)$ the minimum diameter required for a solid driveshaft.

$($b$)$ the maximum inside diameter permitted for a hollow driveshaft if the outside diameter is $\backslash ($ D$=2\mathrm{.}25\backslash$mathrm$\{$in$\}\backslash ).$

$($c$)$ the percent savings in weight realized if the hollow shaft is used instead of the solid shaft.

Part $1$

Correct

Calculate the torque $\backslash ($ T $\backslash )$ in the driveshaft.

Answer: $\backslash ($ T$=\backslash )\backslash (\backslash$mathrm$\{$lb$\}-\backslash$mathrm$\{$ft$\}\backslash ).$

Attempts: $1$ of $5$ used

Part $2$

Incorrect

The elastic torsion formula can be manipulated to determine a relationship between shaft diameter, maximum shear stress, and torque. The minimum allowable diameter is the diameter at which the maximum shear stress in the shaft equals the allowable shear stress. Be careful with units.

Determine the minimum diameter $\backslash ($ d $\backslash )$ required for a solid driveshaft.

Answer: $\backslash ($ d$=\backslash )$

Hint

Assistance Used

Attempts: $2$ of $5$ used

Part $3$

Correct

Determine the maximum inside diameter, $\backslash ($ d$\_\{\backslash$text $\{$in $\}\}\backslash ),$ permitted for a hollow driveshaft if the outside diameter is $\backslash ($ D$=2\mathrm{.}25\backslash )$ in$.$ The elastic torsion formula can be manipulated to determine a relationship between shaft diameter, maximum shear stress, and torque. The minimum allowable diameter is the diameter at which the maximum shear stress in the shaft equals the allowable shear stress. Be careful with units.

Determine the minimum diameter $\backslash ($ d $\backslash )$ required for a solid driveshaft.

Answer: $\backslash ($ d$=\backslash )$ in$.$

Correct

Determine the maximum inside diameter, $\backslash ($ d$\_\{\backslash$mathrm$\{$in$\}\}\backslash ),$ permitted for a hollow driveshaft if the outside diameter is $\backslash ($ D$=2\mathrm{.}25\backslash )$ in$.$

Answer: $\backslash ($ d$\_\{\backslash$text $\{$in $\}\}=\backslash )$ in$.$

Attempts: $1$ of $5$ used

Part $4$

Incorrect

The reduction in weight is proportional to the reduction in cross$-$sectional area. Calculate the crosssectional areas for the solid shaft and for the hollow shaft and determine the percent reduction in crosssectional area. This is also the percent reduction in weight.

Determine the percent savings in weight realized if the hollow shaft is used instead of the solid shaft.

Answer: Savings in weight $\backslash (=\backslash )$

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Hint