Problem $11$: A shaper is operated at a frequency of reciprocation of $1\mathrm{.}5$ s$1,$ and is used to machine a $4$ mm layer of material from the top of a rectangular low$-$carbon steel workpiece. The width of the workpiece is $150$ mm and its length is $200$ mm$.$ the tool has a major cutting$-$edge angle of $30$ degrees and is contacting the workpiece for $72\%$ of the time. The feed is $0\mathrm{.}25$ mm$.$ Find:

a$.$ The un$-$deformed chip thickness

b$.$ The total time to complete the operation neglecting setup, loading and unloading

c$.$ The metal removal rate during machining

d$.$ The power required during machining $($use Figure $1\mathrm{.}52$ to obtain the specific cutting energy$)$