Problem Statement: You are designing the shaft for an alternator of an engine as shown below, and you are

considering the worst$-$case$-$scenario. Your engine is a $302$ ci Coyote and it provides $425$

$lbf-ft$ of torque at the crank. The crank pulley has a diameter of $6\mathrm{.}5$ inches. The alternator

pulley has a diameter of $3$ inches and the alternator pulley shaft is $3$ inches long. Given

that the pulley shafts are made of steel with a yielding shear stress of $29$ ksi and a shear

modulus of $8700$ ksi $,$ and that a factor of safety of $3$ is desired, determine the following:

Problem Queries:

$20$ pts$.$ a$)$ What is the belt tension given that the crank torque and crank pulley diameter are known?

Assume one side of the belt is completely slack and the other side is completely tensioned.

$($Hint: Draw the FBD with tension from both sides and consider the tension on one side as

zero.$)$

$20$ pts$.$ b$)$ What is the torque at the alternator given the belt tension and alternator pulley diameter?

$20$ pts$.$ c$)$ What diameter shaft is needed to provide the desired factor of safety?

$20$ pts$.$ d$)$ What is the angle of twist of the alternator's shaft?

$20$ pts$.$ e$)$ Describe two ways you could reduce the angle of twist.

Known Parameters: