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 9.0 cm .

Part A

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

Express your answer with the appropriate units.

Explanation / Answer

radius of hemisphere, r= 9/2

= 4.5 cm

= 0.045 m

volume of hemispere, V = (2/3)*pi*r^3

= (2/3)*pi*0.045^3

= 1.908*10^-4 m^3

Let M is of heaviest rock that is to be placed.

In the equilibrium net force on the hemosphere = 0

B - m*g - M*g = 0 (here B is buoynat force)

B = m*g + M*g

rho_water*V*g = m*g + M*g

rho_water*V = m + M

==> M = rho_water*V - m

= 1000*1.908*10^-4 - 16*10^-3

= 0.1748 kg or 174.8 grams <<<<<<<<------------Answer

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