Question $1$:

When a person ice skates, the surface of the ice actually melts beneath the blades, so that he or she skates on a thin sheet of water between the blade and the ice.

$($a$)$ Find an expression for total friction force on the bottom of the blade as a function of skater velocity $V,$ blade length $L,$ water thickness $($between the blade

and the ice$)h,$ water viscosity $,$ and blade width $W.$

$($b$)$ Suppose an ice skater of total mass $m$ is skating along at a constant speed of $V_0$ when she suddenly stands stiff with her skates pointed directly forward,

allowing herself to coast to a stop. Neglecting friction due to air resistance, how far will she travel before she comes to a stop? $($Remember$,$ she is coasting on

two skate blades.$)$ Give your answer for the total distance travelled, $x,$ as a function of $V_0,m,L,h,,$ and $W.$

$($c$)$ Find $x$ for the case where $V_0=4\mathrm{.}0\frac{m}{s},m=100kg,L=30cm,W=5\mathrm{.}0mm,$ and $h=0\mathrm{.}10mm.$ Do you think our assumption of negligible air resistance is a

good one?

$($d$)$ Write a python$/$MATLAB code for computing the distance $x$ as a function of $V_o$ and $m,$ keeping all other parameters constant. Take six $V_o$ values between $2$

$\frac{m}{s}$ and $20\frac{m}{s},$ for six different people of $m=50,60,80,110,130,$ and $150kg.$ Plot a three dimensional plot with $m$ on the first axis, $V_0$ as the second axis and

$x$ as the third axis.