On a sunny day, you and your physics-major friend, Sally Geek, go to an ice crea

Question

On a sunny day, you and your physics-major friend, Sally Geek, go to an ice cream shop. The cone you are given is filled with melted ice cream of density 1.2 g/cm3 . The diameter of the cone is 6 cm at the wide end and is 10 cm deep. Sally wants you to find the pressure at the bottom of the cone. Suddenly she makes a small hole of diameter 1 mm at the bottom of the cone. The ice cream starts to leak. She says find the amount of time it takes the ice cream to run out. Please show all work and explanation. Thanks.

Explanation / Answer

Area of wide end = (pi r^2), = 28.278cm^2.

Volume of cone = 1/3(area x depth), = 94.26cc.

Mass in cone = (94.26 x 1.2) = 113.112g, or 0.113112kg.

1.2g/cc = 1,200kg/m^3.

The con height is 10cm. (0.1 metre)

(1,200 x 9.8) = 11,760N.

(11,760 x 0.1) = 1,176Pa.

The area of a 1mm. hole is 0.7855mm^2.

In order to have 1mm diameter hole, you must cut to bottom part.

So, let's find how long to be cut: 6cm / 10 cm = 1mm / cut-part cut-part = 10/6 = 1.67 mm

So, the height of the cone now is 10cm-1.67mm = 9.833 cm

P = rho . g . h = 1.2 x 10 x 9.833 10^-3 = 0.118 N/cm^2 = 1180 N/m2 or 1180 pascal

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