$28\mathrm{.}5$R $($USCS units$)$ An axle$-$bearing surface made of high carbon steel has worn beyond its useful life. When it was new, the diameter was $4\mathrm{.}00$ in $.$ The length of the bearing surface is $7\mathrm{.}0$ in $.$ In order to restore it$,$ the diameter is turned to $3\mathrm{.}90$ in to provide a uniform surface. Next the axle is built up so that it is oversized by the deposition of a surface weld bead, which is deposited by rotating the axle at $3\mathrm{.}0re\frac{v}{m}in$ on the lathe and feeding the welding head along the surface as in a turning operation. The weld metal deposited is a similar composition to the steel in the axle. The weld bead height is $\frac{3}{32}$ in above the original surface. In addition, the weld bead penetrates $\frac{1}{16}$ in into the surface of the axle. The width of the weld bead is $0\mathrm{.}25$ in ; thus, the feed on the lathe was set to $0\mathrm{.}25i\frac{n}{r}ev.$ After the surface weld is applied, the axle is turned again to achieve the original diameter of $4\mathrm{.}00$ in $.$ Assuming the heat transfer factor was $0\mathrm{.}80$ and the melting factor was $0\mathrm{.}65,$ determine $($a$)$ the relative velocity between the workpiece and the welding head, $($b$)$ the rate of heat generated at the welding source, and $($c$)$ how long it took to complete the welding portion of this operation.