One day when you come into physics lab you find several plastic hemispheres floa

Question

One day when you come into physics lab you find several plastic hemispheres floating like boats in a tank of fresh water. Each lab group is challenged to determine the heaviest rock that can be placed in the bottom of a plastic boat without sinking it. You get one try. Sinking the boat gets you no points, and the maximum number of points goes to the group that can place the heaviest rock without sinking. You begin by measuring one of the hemispheres, finding that it has a mass of 16 g and a diameter of 8.8 cm .

Part A

What is the mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat?

Explanation / Answer

the volume of a hemisphere is (pi/12)D^3

density of water = d = 1000 kg/m^3

then mass of water dispalced by hemisphere is density *volume = 1000*(pi/12)*D^3

weight of the dispalced water = 1000*(pi/12)*D^3*g = Buoyant force in upward direction

For the floating the down ward force of weight of boat + un kown weight of the rock must be balanced by upward buoyant force

then (mb+mr)*g = 1000*(pi/12)*D^3*g

mass of the rock is mr= 1000*(pi/12)*D^3 - mb

mr = 1000*(3.142/12)*(0.088)^3 - 0.016 = 0.162 kg = 162 g

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