$[0\mathrm{.}5/2$ Points$]$

SERPSE$106.$XP$.007.$

One popular design of a household juice machine is a conical, perforated stainless steel basket $3\mathrm{.}30$ cm high with a closed bottom of diameter $8\mathrm{.}00$ cm and open top of diameter $13\mathrm{.}40$ cm that spins at $20500$ revolutions per minute about a vertical axis. Solid pieces of fruit are chopped into granules by cutters at the bottom of the spinning cone. Then the fruit granules rapidly make their way to the sloping surface where the juice is extracted to the outside of the cone through the mesh perforations. The dry pulp spirals upward along the slope to be ejected from the top of the cone. The juice is collected in an enclosure immediately surrounding the sloped surface of the cone.

$($a$)$ What centripetal acceleration does a bit of fruit experience when it is spinning with the basket at a point midway between the top and botiom? $\frac{m}{s^{?}}$

$($b$)$ Observe that the weight of the fruit is a negligible force. What is the normal force on $2\mathrm{.}00$ g of fruit at that point?

$9\mathrm{.}28e+05N$

$($c$)$ If the effective coefficient of kinetic friction between the fruit and the cone is $0\mathrm{.}580,$ with what acceleration relative to the cone will the bit of fruit start to slide up the wall of the cone at that point, after being temporarily stuck?

$0\mathrm{.}58\frac{m}{s^2}($radially up the wall of the cone$)$