One popular design of a household juice machine is a conical, perforated stainless steel basket 3.30 cm high with a closed bottom of diameter 8.00 cm and open top of diameter 13.40 cm that spins at 23000 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. Pulp Motor Spinning basket Juice spout (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 bottom? m/s² ---Direction--- (b) Observe that the weight of the fruit is a negligible force. What is the normal force on 1.50 g of fruit at that point? N (c) If the effective coefficient of kinetic friction between the fruit and the cone is 0.580, 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? m/s² (radially up the wall of the cone)

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One popular design of a household juice machine is a conical, perforated stainless steel basket 3.30 cm high with a closed
bottom of diameter 8.00 cm and open top of diameter 13.40 cm that spins at 23000 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.
Pulp
D
Motor
Spinning
basket
Juice spout
(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 bottom?
m/s² ---Direction---
(b) Observe that the weight of the fruit is a negligible force. What is the normal force on 1.50 g of fruit at that
point?
N
(c) If the effective coefficient of kinetic friction between the fruit and the cone is 0.580, 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?
m/s2 (radially up the wall of the cone)
Transcribed Image Text:One popular design of a household juice machine is a conical, perforated stainless steel basket 3.30 cm high with a closed bottom of diameter 8.00 cm and open top of diameter 13.40 cm that spins at 23000 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. Pulp D Motor Spinning basket Juice spout (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 bottom? m/s² ---Direction--- (b) Observe that the weight of the fruit is a negligible force. What is the normal force on 1.50 g of fruit at that point? N (c) If the effective coefficient of kinetic friction between the fruit and the cone is 0.580, 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? m/s2 (radially up the wall of the cone)
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