a piece of metal with density 6.4g/cm has the shape of a hockey puck, with a dia
ID: 1506698 • Letter: A
Question
a piece of metal with density 6.4g/cm has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.3 cm. If the puck is placed in a bath of fluid with density 10 g/cm^3, it's floats. A piece of metal with density 6.4 g/cm3 has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.3 cm. If the puck is placed in a bath of fluid with density 10 g/cm3, it floats. (a) How deep below the surface of the fluid is the bottom of the metal puck? (b) A small cube made of the same metal as the puck and with sides of length 0.95 cm is attached to the center of the puck. The puck is then inserted into the fluid, submerging the side that the cube is on. How deep below the surface of the fluid is the bottom of the metal cube?Explanation / Answer
piece of metal with density
as the shape of a hockey puck, with a diameter of
density of fluid is 10 g/cc
density of metal is 6.4 g/cc
the weight of the displaced liquid equals the weight of the lead puck
the 'hole' in the liquid has the same shape as the lead puck, of course
so the only difference will be in the heights of the 'hole' and the puck
and the masses/weights are proportional to volumes
from D = m/V
m = D V = D (A h) {{V - base area x height}}
masses are equal so
(D A h) mercury = (D A h) lead
A's are equal so cancel
10h = 6.4 (2.3)
h = 1.47 cm to two sig figs
(b)As another metal is of same mass and density it will also go the same deep.
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