DESIGN PROJECTS

$5\mathrm{.}101$ A step$-$cone pulley with a belt drive $($Fig$.5\mathrm{.}67)$ is used to change the cutting speeds in a lathe.

The speed of the driving shaft is $350$ rpm and the speeds of the output shaft are $150,250,$

$450,$ and $750$ rpm $.$ The diameters of the driving and the driven pulleys, corresponding to

$150$ rpm output speed, are $250$ mm and $1000$ mm $,$ respectively. The center distance between

the shafts is $5$ m $.$ The mass moments of inertia of the driving and driven step cones are $0\mathrm{.}1$

and $0\mathrm{.}2kg-m^2,$ respectively. Find the cross$-$sectional area of the belt to avoid resonance with

any of the input$/$output speeds of the system. Assume the Young's modulus of the belt mate$-$

rial as ${10}^{10}\frac{N}{m^2}.$

Please explain step by step from formulation to solving