17857.14285714286`
0.9999440031358243`


Plot[f/(1+f),{f,0,10},GridLinesStyle->LightGray,PlotStyle->{
{Thickness[0.005],Blue}},
PlotRange->{{0,10},{0.,1}},
FrameLabel->{
{Style["δ",24,Black,FontFamily->"Helvetica"], None},
{Style["𝒻 ",24,FontFamily->"Helvetica"], None}
},
GridLinesStyle->LightGray,PlotTheme->"Grid",Frame->True,
FrameTicksStyle->Directive[Black, 24,FontFamily->"Helvetica"],
Frame->True,
Background -> White,
AspectRatio->0.8,
ImageSize->700,
LabelStyle->Directive[20,FontFamily->"Helvetica"],
PlotLabel->Style["Fraction KE lost ",32,FontFamily->"Helvetica"]]

LogLogPlot[f/(1+f),{f,0.01,1000},GridLinesStyle->LightGray,PlotStyle->{
{Thickness[0.005],Blue}},
PlotRange->{{0.01,1000},{.01,1}},
FrameLabel->{
{Style["δ",24,Black,FontFamily->"Helvetica"], None},
{Style["𝒻 ",24,FontFamily->"Helvetica"], None}
},
GridLinesStyle->LightGray,PlotTheme->"Grid",Frame->True,
FrameTicksStyle->Directive[Black, 24,FontFamily->"Helvetica"],
Frame->True,
Background -> White,
AspectRatio->0.8,
ImageSize->700,
LabelStyle->Directive[20,FontFamily->"Helvetica"],
PlotLabel->Style["Fraction KE lost ",32,FontFamily->"Helvetica"]]

Plot[1/(1+f),{f,0,10},GridLinesStyle->LightGray,PlotStyle->{
{Thickness[0.005],Blue}},
PlotRange->{{0,10},{0.,1}},
FrameLabel->{
{Style["δ",24,Black,FontFamily->"Helvetica"], None},
{Style["𝒻 ",24,FontFamily->"Helvetica"], None}
},
GridLinesStyle->LightGray,PlotTheme->"Grid",Frame->True,
FrameTicksStyle->Directive[Black, 24,FontFamily->"Helvetica"],
Frame->True,
Background -> White,
AspectRatio->0.8,
ImageSize->700,
LabelStyle->Directive[20,FontFamily->"Helvetica"],
PlotLabel->Style["Fraction KE lost ",32,FontFamily->"Helvetica"]]

LogLogPlot[1/(1+f),{f,0.1,10000},GridLinesStyle->LightGray,PlotStyle->{
{Thickness[0.005],Blue}},
PlotRange->{{0.1,10000},{.0001,1}},
FrameLabel->{
{Style["α",24,Black,FontFamily->"Helvetica"], None},
{Style["𝒻 ",24,FontFamily->"Helvetica"], None}
},
GridLinesStyle->LightGray,PlotTheme->"LogGrid",Frame->True,
FrameTicksStyle->Directive[Black, 24,FontFamily->"Helvetica"],
Frame->True,
Background -> White,
AspectRatio->0.8,
ImageSize->700,
LabelStyle->Directive[20,FontFamily->"Helvetica"],
PlotLabel->Style["(final/initial) velocity ",32,FontFamily->"Helvetica"]]

LogLogPlot[f/(1+f),{f,0.1,10000},GridLinesStyle->LightGray,PlotStyle->{
{Thickness[0.005],Blue}},
PlotRange->{{0.1,10000},{.1,1}},
FrameLabel->{
{Style["δ",24,Black,FontFamily->"Helvetica"], None},
{Style["𝒻 ",24,FontFamily->"Helvetica"], None}
},
GridLinesStyle->LightGray,PlotTheme->"LogGrid",Frame->True,
FrameTicksStyle->Directive[Black, 24,FontFamily->"Helvetica"],
Frame->True,
Background -> White,
AspectRatio->0.8,
ImageSize->700,
LabelStyle->Directive[20,FontFamily->"Helvetica"],
PlotLabel->Style["Fraction KE lost ",32,FontFamily->"Helvetica"]]