Problem $2$

A single U$-$groove weld is used to join two pieces of $6\mathrm{.}0-$mm$-$thick austenitic stainless steel plate using an arc welding operation. The radius of the groove is $2\mathrm{.}5$ mm ; however, during welding the penetration of the weld causes an additional $1\mathrm{.}25$ mm of metal to be melted. The length of the weld $=250mm.$ The melting factor of the setup $=0\mathrm{.}65,$ and the heat transfer factor $=0\mathrm{.}90.$ Assuming the resulting top surface of the weld bead is flush with the top surface of the plates, determine $($a$)$ the amount of heat $($in joules$)$ required to melt the volume of metal in this weld $($filler metal plus base metal$),($b$)$ the welding time if the source power is $2500$ W $?$