Activity $4$:

You have completed the tasks that your boss left you to do prior to his return, so you now have lime to resume your normal activities in Automotive Design Support. The R$8$D department have requested some hand calculations to support their development work, in which they are experimenting with a range of drive shaft materials.

Task $4$:

a$)$ An internal combustion engine of $100$ horsepower $($hp$)$ transmits power to the car wheels of an automobile at $600$ revimin $(1$ pm $).$ Neglecting any transmission losses, determine the minimum pernissible diameter of the solid crcular section steel shaft if the maximum shear stress in the shaft is Imited to $75$ MPa $.$ What will be the resulting angle of twist of the shaft, due to the applied torque, over a length of $1$ m $?$ Given that the rigidity modulus, $G=50$GPa. $($Note that $1hp=745\mathrm{.}7W).$

b$)$ If the shaft in $4$ a was replaced by a hollow tube of the same external diameter, but of wall thickness $0\mathrm{.}01$ m $,$ what would be the maximum shear stress in the shaft due to the same applied torque, and the resulting twist of the shaft? The material properties of the shaft may be assumed to be the same as that above.

The research department is experimenting with alternative materials for a solid shaft and they have asked you to previde an ingut too.

c$)$ Using a mystery material, the resulting angle of twist was found to be approximately $2\mathrm{.}5$ degrees. Assuming the same conditions from question $4$ a for the solid bar give two suggestions of what this mystery material could be$.$

Potentiol answers should haye rigidity medulus of approximately $80$ GPa $($accept $50-100$GPa $)$ answers could be Berylium Copper but this is an unsuitable material, more likely to be a form of cast iren, or other irons, structural steel or Inconol.