Design a centrifugal clutch to provide a torque of $2400$ Nm when the rotational speed reaches $870$ rpm using sector weights having the geometry shown in Figure $2.$ Preferred characteristics are that initial contact between weights and drum occur at between $220$ and $230$ rpm and that the width of the weights be less than $30$ cm$.$ Assume a lining coefficient of friction of $0\mathrm{.}3$ and design for an inside drum radius a $($minus the lining thickness$)$ of $15$cm$,$ displacement $\backslash$delta of $3$ mm for the segments to contact the drum, and a static deflection of $1$ mm$.$ The segments are to be made from an iron alloy having a nominal density of $7880$ kg$/$m$3,$ and a safety factor of $3\mathrm{.}5$ is mandated. Hold the weights against their rest position with a force $1\mathrm{.}2$ times their weight. Maximum lining pressure of less than $440$ kPa is preferred.