A block of wood of mass 204 kg floats on water the volume of the wood is 2.0 32 metre cube find the volume of the volume below surface of water dinisty of water 100kg metre cube
Answers
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12-1
12.1. IDENTIFY: Use Eq. (12.1) to calculate the mass and then use w mg = to calculate the weight.
SET UP: ρ = m V/ so m V = ρ From Table 12.1, 3 3 ρ =.× 7 8 10 kg/m .
EXECUTE: For a cylinder of length L and radius R,
2 2 43 V RL ( ) (0.01425 m) (0.858 m) 5.474 10 m . π π − = = =×
Then 3 3 43 m Vρ (7 8 10 kg/m )(5 474 10 m ) 4 27 kg, − = = .× . × = . and
2
w mg == = (4.27 kg)(9.80 m/s ) 41.8 N (about 9.4 lbs). A cart is not needed.
EVALUATE: The rod is less than 1m long and less than 3 cm in diameter, so a weight of around 10 lbs
seems reasonable.
12.2. IDENTIFY: The volume of the remaining object is the volume of a cube minus the volume of a cylinder,
and it is this object for which we know the mass. The target variables are the density of the metal of the
cube and the original weight of the cube.
SET UP: The volume of a cube with side length L is 3L , the volume of a cylinder of radius r and length L
is 2 πr L, and density is / . ρ = m V
EXECUTE: (a) The volume of the metal left after the hole is drilled is the volume of the solid cube minus
the volume of the cylindrical hole:
3 2 3 2 3 43 V L rL π π (5.0 cm) (1.0 cm) (5.0 cm) 109 cm 1.09 10 m . − =− = − = = × The cube with the hole has
mass 2
7 50 N 0 765 kg 9 80 m/s
w m g
. = = =. . and density 3 3
4 3
0.765 kg 7.02 10 kg/m . 1.09 10 m
m
V ρ − == = ×
×
(b) The solid cube has volume 3 3 43 V L 125 cm 1.25 10 m − == = × and mass
3 3 43 m Vρ (7.02 10 kg/m )(1.25 10 m ) 0.878 kg. − == × × = The original weight of the cube was
w mg = =. 8 60 N.
EVALUATE: As Table 12.1 shows, the density of this metal is close to that of iron or steel, so it is
reasonable.
12.3. IDENTIFY: ρ = m V/
SET UP: The density of gold is 3 3 19 3 10 kg/m . . ×
EXECUTE: 3 3 3 63 V (5.0 10 m)(15.0 10 m)(30.0 10 m) 2.25 10 m . −−− − =× × × = ×
3 3
6 3
0.0158 kg 7.02 10 kg/m . 2.25 10 m
m
V ρ − == = ×
×
The metal is not pure gold.
EVALUATE: The average density is only 36% that of gold, so at most 36% of the mass is gold.
12.4. IDENTIFY: Find the mass of gold that has a value of 6 $1 00 10 . . × Then use the density of gold to find the
volume of this mass of gold.
SET UP: For gold, 3 3 ρ = .× 19 3 10 kg/m . The volume V of a cube is related to the length L of one side by
3 V L = .
FLUID MECHANICS
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