BUOYANT
FORCE
INTRODUCTION
Buoyancy is the ability to float. Buoyancy forces are
formed by a principle called Archimedes principle. Archimedes principle said
that buoyancy forces is directly proportional with drowned volume.
Mathematically, Buoyancy force is: F = ρ . g . V, where ρ is the density of fluid (water), g is gravity, and V
is volume which is drowned.
Any object that is completely or partially submerged in a fluid is
buoyed up by a force equal to the weight of the fluid displaced by the body.
Everyone has experienced Archimedes’s principle. As an example of a common
experience, recall that it is relatively easy to lift someone if the person is
in a swimming pool whereas lifting that same individual on dry land is much harder.
Evidently, water provides partial support to any object placed in it. The
upward force that the fluid exerts on an object submerged in it is called the
buoyant force.
According to the Archimedes’s principle, the magnitude of the buoyant
force always equal to the weight of the fluid displaced by the object. The
buoyant force acts vertically upward through what was the centre of gravity of
the displaced fluid.
F = W
Where
F is the buoyant force and W is the weight of the displaced fluid. The units of
the buoyant force and the weight are Newton (N).
The buoyant force acting on the
steel is the same as the buoyant force acting on a cube of fluid of the same
dimensions. This result applies for a submerged object of any shape, size, or
density.
Figure
1: Direction of buoyant force
BUOYANCY FORCE
The boat can float on water based on
this principle. Boat has hull to get buoyancy force and makes the boat float.
So, it is very important to keep hull safe. In the sea, corals are sometimes
found in the sea. Hull can causes the boat drowned since hull is the source of
buoyancy force.
ENGAGE
Figure
2: Examples of application in buoyant force
·
What is buoyant force?
·
How buoyant force
determine whether an object sinks or floats on water?
·
Is there any different
if the boat is floating on fresh water and salt water.
·
What factors that
influence buoyant force?
·
What principle related
to buoyant force?
EMPOWER
Planning and doing an experiment:
Title :
The effect of mass of different objects on the buoyant force.
Objective :
a)
Use a Force Sensor to measure the
weights of objects in and out of water
b)
Determine the weight of water displaced by each of the objects
c)
Determine the relationship of depth of the immersed object to the
buoyant force.
Hypothesis :
The magnitude of the buoyant force is directly proportional to the
weight of the fluid that the object displaces.
Procedures :
PART 1 : COMPUTER SETUP
Figure 3 :
Computer Set Up
1. Connect
the Science Workshop interface to the
computer, turn on the interface, and turn on the computer.
2.
Connect
the DIN plug of the Force Sensor to Analog Channel A.
3.
Open the
document titled as shown:
|
DataStudio
|
ScienceWorkshop (Mac)
|
ScienceWorkshop (Win)
|
|
P13 Buoyant Force.DS
|
P18 Buoyant Force
|
P18_BUOY.SWS
|
·
The DataStudio document has a Workbook
display.
·
The ScienceWorkshop document has a Graph
display with Force versus Depth.
·
Data
recording is set for 1 Hz. Keyboard Sampling allows the user to enter the
submerged depth in meters.
PART 2 : SENSOR CALIBRATION AND EQUIPMENT
SETUP
Figure
4: Equipment Set Up
1.
Mount
the Force Sensor on a horizontal rod with the hook end down.
2.
Using
the calipers, measure the diameter of the aluminium cylinder. From the
diameter, calculate the radius and the cross-section area. Record the
cross-section area in the Data Table in the Lab Report section.
3.
Hang the
aluminium cylinder from the Force Sensor hook with a string.
4.
Put
about 800 mL of water into the beaker and place the beaker on the lab jack
below the hanging cylinder. The bottom of the cylinder should be touching the
water.
5.
Position
the metric ruler next to the edge of the lab jack. Note the initial height of
the top of the lab jack.
PART 3 : DATA RECORDING
1.
With the cylinder attached to the Force Sensor hook, press the tare
button on the Force Sensor to zero the sensor.
2.
Record Force vs. Depth data as you submerge the cylinder.
In DataStudio,
move the Table display so you can see it clearly.
• Click on
the ‘Start’ button to start recording data. The ‘Start’ button changes to a
‘Keep’ and a ‘Stop’ button. The Force will
appear in the first cell in the Table display. Click the ‘Keep’ button to
record the force value.
• Immerse
the cylinder 1 millimeters (1 mm or 0.001 m) by raising the beaker of water 1
mm with the lab jack. Use the metric ruler to measure the distance that you
raise the lab jack.
• Click
the Keep button to record the next Force value at the depth of 0.001 m.
• Increase
the depth of submersion by increments of 1 mm. After each increase in the
submersion, wait for the force reading in the display to stabilize, then click
the Keep button to record a Force value at the appropriate depth.
• Repeat
the data recording procedure until the top of the cylinder is submerged. Stop
data recording by clicking on the ‘Stop’ button. Run #1 will appear in the
Summary window.
In ScienceWorkshop,
click the ‘REC’ button to begin collecting data.
Figure 3 : Keyboard Sampling
• The
‘Keyboard Sampling’ window will open. Move it so you can also see the Digits
display. The default value for ‘Entry #1’ is 10.000.
• Because
the cylinder is not submerged, type in ‘0’ as the depth. Click ‘Enter’ to
record the depth and force values. The entered depth value will appear in the
Data list.
• Immerse
the cylinder 1 millimeters (1 mm or 0.001 m) by raising the beaker of water 1
mm with the lab jack. Use the metric ruler to measure the distance that you
raise the lab jack.
• For
‘Entry #2’, type in ‘0.001’ (1 millimeters). Click ‘Enter’ to record the depth
and force values.
• Increase
the depth of submersion by increments of 1 mm. After each increase in the
submersion, wait for the force reading in the Digits display to stabilize, then
click the Enter button to record a Force value at the appropriate depth.
• Repeat
the data recording procedure until the top of the cylinder is submerged. Stop
data recording by clicking the ‘Stop Sampling’ button in the ‘Keyboard
Sampling’ window.
• The
‘Keyboard Sampling’ window will disappear. ‘Run #1’ will appear in the Data
List in the Experiment Setup window.
PART 4 : REPEATITION OF THE PROCEDURE USING DIFFERENT
OBJECTS
•
Repeat
the procedure in part 2 for step 2 with the brass and copper.
Results :
|
|
Aluminium
|
Brass
|
Copper
|
|
Actual mass of sample
(g) |
26.16
|
111.39
|
102.65
|
|
Diameter of sample (g)
|
1.88
|
1.88
|
1.88
|
|
Sample height (cm)
|
3.45
|
4.29
|
4.49
|
|
Density (ρ) H20 (g/cm3)
|
1.00
|
1.00
|
1.00
|
|
Apparent mass in H20 (g)
|
15.25
|
89.26
|
97.30
|
Calculation
:
|
|
Aluminium
|
Brass
|
Copper
|
|
Actual weight of sample (cm/s2)
|
25654.07
|
100664.75
|
109235.72
|
|
Density of sample (g/cm3)
|
2.78
|
8.78
|
9.13
|
|
Area of sample (cm2)
|
2.78
|
2.78
|
2.78
|
|
Volume of cylinder (cm3)
|
9.58
|
11.91
|
12.46
|
|
Displaced liquid volume= Fb
|
9.43
|
11.70
|
12.20
|
Graph 1: Force against depth graph
Discussion :
In this experiment, we study about the
relationship water displaced and buoyancy force. Archimedes principle says that
the buoyant force on a submerged object is equal to the weight of the fluid it
displaces. Thus, in short, buoyancy = weight of displaced fluid. This principle
is useful for determining the volume and therefore the density of an irregularly shaped object by measuring
its mass in air and its effective mass when submerged
in water (density = 1 gram per cubic centimetre). This effective mass under
water will be its actual mass minus the mass of the fluid displaced. The
difference between the real and effective mass therefore gives the mass of
water displaced and allows the calculation of the volume of the irregularly shaped
object. The mass divided by the volume thus determined gives a measure of the
average density of the object. Buoyancy shows that the buoyant force on a volume of
water and a submerged object of the same volume is the same. Since it exactly
supports the volume of water, it follows that the buoyant force on any
submerged object is equal to the weight of the water displaced.
Based on the result of the experiment, we can
see that as the mass of the object increase the volume of the fluid displaced
also increase. This means that the
buoyant force is also increase since the formula for the buoyancy is equal to
the weight of displaced fluid.
For the force against depth graph, we can see
that force is directly proportional to the depth. As the depth of the immersed object increase,
the magnitude of the buoyant force is also increase.
Questions:
1. Why was the Force
Sensor zeroed after the cylinder was attached to the hook?
The force sensor
measures the net force that is the cylinder’s weight (downward force) minus the
buoyant force (upward force). By taring
the force sensor when the cylinder was attached and out of water, the weight
was accounted for during calibration and the sensor will now report only the
buoyant (upward) force.
2.
What is the effects of mass of sample to the buoyant force?
The mass of sample will affect the magnitude
of the buoyant force since formula of the density is the mass over volume.
3.
In that experiment, what the objects give the lowest and highest buoyant
force?
The object that gives the lowest of buoyant
force is the aluminium whereas the object that gives the highest of buoyant
force is the copper. This results depend
on the density of that objects.
Conclusion:
As conclusion, an object that floats
displaces the amount of water that has the same weight as the object. If it
sinks, it displaces an amount of water that has less weight than the object.
ENHANCE
The
application of buoyant force play an
important roles in our daily life. Discuss the important of buoyancy
control in diving?
Answer:
Controlling buoyancy is a key component of your
diving safety. The physics of floating and sinking are simple concepts, yet
achieving practical control of your buoyancy when outfitted with scuba
equipment and immersed in water is an entirely other matter. Each change in
equipment affects your buoyancy. As your dive equipment grows more complex, the
more attention your buoyancy requires. Given its role as a fundamental element
of dive safety, it's no wonder problems with buoyancy control are often the
underlying cause of a dive injury or fatality.
Divers with proper buoyancy control can maintain their position with very little effort. They can descend or ascend at will. In contrast, divers with poor buoyancy-control skills struggle throughout the dive. In extreme situations, major buoyancy-control issues may cause divers to make grave errors such as descending well beyond their planned depth, negatively affecting gas consumption and no-decompression calculations, or on the flip side, uncontrolled ascents, increasing the risk of decompression illness. There is no doubt buoyancy control affects many aspects of dive safety. Experts in dive training, dive medicine and research all know just how integral it is and are always eager to share thoughts on how to develop and maintain good skills.
Training
Good buoyancy begins with proper weighting. It is
imperative the amount of weight you use allows you to descend,
not causes you to do so. Weight placement makes a difference, too. A classic
buoyancy-control device (BCD) is generally configured to require a separate
weight belt, whereas newer BCDs often integrate the weights. Each approach
affects a diver's body position in the water, requiring time and attention to
get comfortable. Using rental gear can complicate the process, especially for
new divers, as each change in configuration, responsiveness and other variables
can alter a diver's comfort and buoyancy. Diving with a dry suit, a weight
harness or a rebreather adds to the complexity.
The BCD is the most complex piece
of scuba equipment a diver must master. To truly master buoyancy control, a
diver must understand his BCD inside and out, including knowing how it reacts
to the addition or venting of air. It requires proper maintenance (see
"Gear," Alert Diver, Spring 2011) to prevent sticking
buttons or leaking bladders. Malfunctioning BCDs can lead to uncontrolled
ascents or descents before a diver even realizes what's happening. Like any
piece of equipment, proper function requires proper maintenance. But lack of
maintenance is not the only concern; operator error can also cause loss of
control. Improperly connecting a low pressure inflator can cause negative
buoyancy without a means to correct it. Hitting the inflator button instead of
the vent button can cause a rapid ascent. Every diver needs to be familiar with
his own equipment as well as his buddy's. In a stressful or emergency situation
there may not be time to search for weight releases or inflator/deflator
valves.
Figure 5
: Diving Training
Dive Medicine
Many do not equate buoyancy skills with dive
medicine, but there is definitely a connection. The most common dive injury is
consistently middle-ear barotraumas. There are certainly many factors that lead
to this injury, but buoyancy issues are often among them. Every diver is taught
that if discomfort is felt during descent to stop the descent, ascend a few
feet or until the discomfort resolves, and then attempt to equalize again. This
is very difficult to execute without good buoyancy control. When experiencing a
reverse block during ascent, a diver should stop the ascent, descend until the
discomfort resolves and attempt ascent again using appropriate equalization manoeuvres.
The ability to stabilize and adjust position in the water column certainly
takes practice, but as a cornerstone skill, it's worth the effort.
Most marine life injuries are due to incidental contact. Proper buoyancy helps divers avoid contact as it maintains necessary distance from marine life. It also prevents the destruction of the reef and the microscopic critters that live on sub aquatic surfaces, as buoyancy control reduces the need to place hands on those surfaces to steady a diver's position. Buoyancy skills not only protect divers but the environment as well.
Finally, one of the most serious
consequences of inadequate buoyancy control is a rapid ascent. This can place a
diver at risk for a lung overexpansion injury (pulmonary barotraumas), and it
also increases the risk of a potentially fatal arterial gas embolism (AGE). The
easiest way to avoid both these injuries is to learn the best method of
prevention good buoyancy.
Figure 6 : Barotraumas Ear
EXTENSION
Figure
7 : Application of buoyant force
The
application of buoyancy can be applied
to staying afloat on the water. In the early 1800s, a young Missippi
River flat-boat operator submitted a patent application describing a device for
“buoying vessels over shoals”. The invention proposed to prevent a problem he
had often witnessed on the river-boats ground on sandbars-by equipping the
boats with adjustable buoyant air chambers. The young man even whittles a model
of his invention, but he was not destined for fame as an inventor; instead
Abraham Lincoln (1809-1865) was famous for much else. In fact Lincoln had a sound idea with his proposal to use buoyant
force in protecting boats from running aground.
Buoyancy on the surface of water has
a number of easily noticeable effects in the real world. (Having established
the definition of fluid, from this point onward, the fluids discussed will be
primarily those most commonly experienced: water and air). It is due to
buoyancy that fish, human swimmers, icebergs, and ships stay afloat. Fish offer
an interesting application of volume change as a means of altering buoyancy: a
fish has an interesting swim bladder, which is filled with gas. When it needs
to rise or descend, it changes the volume in its swim bladder, which then changes
its density. The examples of swimmers and icebergs directly illustrate the
principle of density- on the part of the water in the first instance, and on
the part of the object itself in the second.
To a swimmer, the difference between
swimming in fresh water and salt water shows that buoyant force depends as much
on the density of the fluids as on the volume displaced. Fresh water has a
density of 62.4lb/ft3 (9,925N/m3), whereas that of salt
water is 64lb/ft3 (10,167N/m3). For this reason, salt
water provides more buoyant force than fresh water; in Israel’s Dead Sea, the
saltiest body of water on Earth, bathers experience an enormous amount of
buoyant force.
Water is an unusual substance in a
number of regards, not least its behaviour as it freezes. Close to the freezing
point, water thicken up, but once it turns to ice, it becomes less dense. This
is why ice cubes and icebergs float. However, their low density in comparison
to the water around them means that only part of an icebergs stay atop the
surface. The submerged percentage of an iceberg is the same as the ratio of the
density of ice to that of water: 89%.
UNIQUE
FEATURE OF THIS EXPERIMENT
·
Buoyancy is defined as
the tendency of a fluid to exert a supporting upward force on a body placed in
the fluid.
·
Buoyant force must
equal to the weight of the displaced fluid.
·
A solid object would
float if the density of the solid object were less than the density of the
fluid and vice versa.
References:
Air
Consumption (2012). Retrieved on November 17, 2012 from http://www.saireecottagediving.com/air-consumption/
Buoyant Forces and Archimedes' Principle (2006). Retrieved on November 15, 2012 from http://www.engineering.com/Library/ArticlesPage/tabid/85/ArticleID/205/Buoyant-Forces-and-Archimedes-Principle.aspx
Buoyancy Force application (2011). Retrieved on November 16, 2012 from http://simple-engineering.blogspot.com/2011/08/buoyancy-force-application.html
Experiment P18: Buoyant Force (Force Sensor) (1996).
Retrieved on November 14, 2012 from http://kcyap.home.nie.edu.sg/qcp521/Updated_Experiment1_Buoyant_Force.pdf
J.
Andrew Doyle (1999). Swimming. Retrieved on November 15, 2012 from http://www2.gsu.edu/~wwwfit/swimming.html
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