Physics 151 Class Exercise: Buoyancy - KEY
1. A cube of iron 0.300 m on a side is suspended (in equilibrium) from a large spring scale (which
reads in Newtons) held over a giant tank of water. The center of the cube is 30.00 m below the
surface of the water.
(a) What is the volume of the cube?
(b) What is the mass of the cube?
(c) What is the weight of the water displaced by the cube?
(d) What is the magnitude of the force of buoyancy on the cube?
(e) What is the reading on the spring scale ?
(f) What is the pressure on the top surface of the cube?
(g) What is the pressure on the bottom surface of the cube?
(h) What is the force on the top surface of the cube?
(i) What is the force on the bottom surface of the cube?
(j) What is the difference between the force on the bottom and the force on the top?
(
)
3
33
0.300 0.0270Vl m m== =
()
3
3
7860 0.0270 212
Fe
kg
M
Vmkg
m
ρ
⎛⎞
== =
⎜⎟
⎝⎠
()
3
32
1000 0.0270 9.81 265
Fe
kg m
WVg m N
ms
ρ
⎛⎞ ⎛⎞
== =
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
265
B
F
N
=
()
2
212 9.81 265 1810
B
m
TmgF kg N N
s
⎛⎞
=−= − =
⎜⎟
⎝⎠
()
()
5 5
32
1.013 10 1000 9.81 29.85 3.941 10
a
kg m
PP gh Pa m Pa
ms
ρ
⎛⎞⎛⎞
=+ = × + = ×
⎜⎟⎜⎟
⎝⎠⎝⎠
()
()
5 5
32
1.013 10 1000 9.81 30.15 3.971 10
a
kg m
PP gh Pa m Pa
ms
ρ
⎛⎞⎛⎞
=+ = × + = ×
⎜⎟⎜⎟
⎝⎠⎝⎠
()
()
2
5
3.941 10 0.3 35470FPA Pa m N== × =
()
()
2
5
3.971 10 0.3 35740FPA Pa m N== × =
12
35740 35470 270FFF N N N∆= − = − =
