Republic of the Philippines
Carig Sur, Tuguegarao City
Cagayan State University
CARIG CAMPUS
Tel. No. (078) 304 – 0818
BUOYANCY
1.)
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2.)
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3.)
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4.)
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5.)
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6.)
a.
A piece of metal weighs 350 N in air
and when it is submerged completely in
water it weighs 240 N.
Find the volume of the metal.
Find the specific weight of the metal.
Find the specific gravity of the metal.
A prismatic object 200 mm thick by 200
mm wide by 400 mm long is weighted
in water at a depth of 500 mm and
found to be 50 N.
Find its weight in air.
Find its specific gravity.
Find its specific weight.
Find the weight of a certain crown in air
is 14 N and its weight in water is 12.7
N. Assuming that the crown is an alloy
of gold (SG=19.3) and silver (SG=10.5).
Assume unit weight if water equal to
9.79 kN/m^3.
Compute the volume of the crown.
Compute the specific gravity of the crown.
Compute the fraction of silver in the crown.
A wooden buoy of SG=0.75 floats in a
liquid with SG of 0.85.
What is the percentage of the volume above
the liquid surface to the total volume of the
buoy?
If the volume above the liquid surface is
0.0145 m^3, what is the weight of the
wooden buoy?
What load that will cause the buoy to be fully
submerged?
5.a. What fraction of the volume of a
solid object of SG=7.3 floats above the
surface of a container of mercury?
If the volume of the object below the liquid
surface is 0.014 m^3, what is the weight of
the object.
What load applied vertically that would
cause the object to be fully submerged?
A block of wood 0.6m x 0.6m x “h”
meters in dimension was thrown into
the water, it floats with 0.18 m
projecting above the water surface. The
same block was thrown into a container
of a liquid having a SG=0.90 and it
floats with 0.14 cm projecting above the
liquid surface.
Determine the value of “h”.
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b. Determine the specific gravity of the block.
c. Determine the weight of the block.
7.)
A piece of wood floats in water with
50mm projecting above the water
surface. When placed in glycerin of
SG=1.35, the block projects 75mm
above the liquid surface.
a. Find the height of the piece of wood.
b. Find the specific gravity of the wood.
c. Find the weight of the wood if it has a cross
sectional area of 200mm x 200mm.
8.)
A block of wood with a horizontal
section of 0.40m x 0.40m floats in water
with 0.20m projecting above the water
surface. If this block is placed in a body
of oil having a SG of 0.80, it floats with
0.18m projecting above the oil surface.
a. Determine the height of the object.
b. Determine the specific gravity of the object.
c. Determine the weight of the object.
9.)
A prismatic object has a weight of 500N
in air, when the object is completely
submerged in a liquid of SG=0.86, it
weighs 450N.
a. Compute the volume of the object.
b. Compute the specific weight of the object.
c. Compute the specific gravity of the object.
10.) An object having a SG of 0.60 floats in
a liquid having a SG of 0.80.
a. What is the percentage of the volume below
the liquid surface to the total volume of the
body?
b. If the volume above the liquid surface is
0.024 m^3, what is the weight of the object?
c. What is the load that will cause the object to
be fully submerged?
11.) A tank with vertical sides is 1.5m
square, 3.5m depth is filled to a depth
of 2.8m of a liquid having a SG of 0.80.
A cube of wood having a SG of 0.60
measuring 1 m on an edge is placed on
the liquid.
a. Find the weight of the volume of the liquid
displaced.
b. By what amount will the liquid rise on the
tank?
c. What will be the forced increased on one side
of the tank?
12.) A container holds two layers of different
liquids, one fluid having a specific
gravity of 1.2 is 200 mm deep and the
Republic of the Philippines
Carig Sur, Tuguegarao City
Cagayan State University
CARIG CAMPUS
Tel. No. (078) 304 – 0818
other fluid having a specific gravity of
1.5 is 250mm deep. A solid spherical
metal having a diameter of 225 mm and
a SG of 7.4 is submerged such a manner
that half of the sphere is on the top layer
and the other half in the bottom layer of
fluids.
a. Compute the weight of the spherical metal.
b. Compute the buoyant force acting on the
object.
c. Compute the tension in the wire holding the
sphere to maintain its position.
13.) Two spheres each 1.20 m in diameter
are connected by means of a short rope.
One weighs 4kN and the other weighs
12Kn. When placed in water.
a. Compute the tension in the rope.
b. Compute the depth of floatation of the 4Kn
sphere.
c. Compute the volume of sphere exposed
above the water surface.
14.) A hollow cylinder 1.0m in diameter and
2 m long weighs 3825N.
a. How many kN of lead weighing 110 kN/m^3
must be fastened to the outside bottom to
make the cylinder float vertically with 1.50 m
submerged in fresh water.
b. How many kN of lead weighing 110 kN/m^3
must be placed inside the cylinder to make
the cylinder float vertically with 1.50 m
submerged in fresh water.
c. What additional load must be placed inside
the cylinder to make the top of the cylinder
flush with the water surface.
15.) A concrete block with a volume of 0.023
m^3 is tied to one end of a wooden post
having dimensions of 200 mm x 200
mm by 3m long and placed in fresh
water. Weight of wood is 6.4 kN/m^3
and that of concrete is 23.5 kN/m^3.
a. Determine the length of the wooden post
above the water surface.
b. Determine the volume of additional concrete
to be tied to the bottom of the post to make
its top flush with the water surface.
c. Determine the total weight of concrete to
make its top flush with the water surface.
16.) A rectangular barge weighing 200000
kg is 14 m long, 8 m wide and 4.5 m
deep. It will transport to Manila 20mm
diameter, 6 m long steel reinforcing bars
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having a density of 7850 kg/m^3.
Density of salt water is 1026kg/m^3.
a. Determine the draft of the barge on sea
water before the bars was loaded.
b. If a draft is to be maintained at 3 m, how
many pieces of steel bars could it carry?
c. What is the draft of the barge when one half
of its cargo is unloaded in fresh water?
17.) A cubical block having an edge equal to
3m has its upper half of SG 0.80 and its
lower half of SG 1.40. It is resting on a
two-layer fluid with an upper SG of 0.90
and a lower SG of 1.20.
a. Compute the total weight of the cube in
quintals.
b. Compute the height of the top of the cube
above the interface of the two-layer fluid.
c. If the depth of the upper layer of fluid having
a SG of 0.90 is equal to 1.20 m, how far
below the liquid surface is the top of the cube.
18.) A concrete cube 0.5 m on each side is to
be held in equilibrium under water by
attaching a light foam buoy to it.
Specific weight of concrete and foam
are 23.58 kN/m^3 and 0.79 kN/m^3
respectively. Assume unit weight of
water = 9.79 kN/m^3.
a. What is the minimum volume of foam
required?
b. What is the weight of the foam?
c. What is the total weight of the concrete and
foam?
19.) A piece of wood of SG 0.651 is 3 in.
square and 5 ft. long.
a. What is the volume of lead having a unit
weight of 700 pcf that should be fastened at
one end of the stick so that it will float upright
in 1 ft. out of water?
b. Determine the weight of the lead?
c. Determine the total weight of lead and the
wood.
20.) A circular log having a diameter of 8ft
has a length of 15 ft. It has a specific
gravity of 0.425.
a. Determine the weight of the log.
b. To what depth will the log sink in fresh water.
c. What load must be applied in order to
submerged the log fully?