S M K Pahi
LESSON 3.5 - Application Archimedes Principal
(4) Sketch the following graph:
LESSON 3.5 - Applying Archimedes’
principle.
(a) Introduction.
The figure shows a load of mass 40 N suspended in
air whereas the others show the same load immersed
in water at four differents depth.
(b) Archimedes’ Principle
Archimedes’ Principle state that “ When an object is
immersed in a fluid (a liquid or a gas) ,the buoyant
force ( upthrust force) on the object is equal in size to
the weight of fluid displaced by the object.
Density and Buoyancy(keapungan)
Estimate the spring balance readings for each figure
and make the conclusion:
(1) When an object is immersed partially or
completely in a fluid, the weight of the object
reduce and it is called as apparent weight.
From Archimedes’s Principle :
Buoyant Force = Weight of fluid displace
= mg
(note : F = ma)
= ρVg
(note : ρ = m )
V
Thus FB = ρ V g
(2) The apparent weight depends on the weight of
water dispersed/displaced.
(3) The apparent weight is caused by an
upward force exerted by the fluid on the object
and the force is known as Buoyance Force
Or
Where FB = Bouyant Force or Upthrust
ρ = Density of fluid
V = Volume of fluid displaced or the
volume of the object that
immersed in the fluid.
1
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
Buoyant Force and Flotation
Example 1
A metal sphere has a volume 5 x 10-4 m3 is
immersed in water of density 1 x 103 kgm-3.
Determine the upthrust experienced by the sphere?
Solution
If
Example 2
A wooden block with a density 4 x 10 3 kg m-3 and
a mass of 5 kg is immersed in a liquid of density
1 x 103 kg m - 3. Calculate the buoyant force acting on
the wooden block?
Buoyant force = weight ⇒ the object floats
and stationary
Buoyant force > weight ⇒ the object moves
up
Buoyant force < weight ⇒ the object moves
down
The Law of Flotation
A floating object displaces its own weight of fluid in
which it floats.
Solution
Example 4
An object of mass 5 kg floats on the surface water.
What is the upthrust experienced by the object.
Solution
Example 3
An object has a weight of 40 N in air and 36 N in a
liquid of density 800 kgm-3 . Determine the volume of
the object.ialah 36 N?
Solution
2
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
Example 5
Application of Archimedes’ Principle
Based on Figure (a), (b) ,(c) and (d) write the
equations in words to relate the forces acting on the
objects when the objects float and stationary.
(1)
Ship
A ship , though very heavy , floats on the
surface of the sea.
This is because the buoyant force = the weight
of the ship.
The buoyant force acting on the ship is large
enough because the ship is hollow and the
volume of water displaced by the ship is
sufficiently large. ( FB = ρV g)
The density of sea water varies with location
and season. To ensure that a ship is loaded
within safe limits , the Plimsoll line marked on
the body of the ship acts as a guide.
Solution
(2) Submarine
Example 5
The figure shows a glass tube of mass 0.012 kg with
uniform diameter and cross-sectional area 4 x 10-4 m2
, and it is filled with sand so that it is made vertical in
a beaker containing water.
[ Density of water is 1000 kg m-3 ]
A submarine can sail on the surface or
underneath it. Its outer hull is entirely watertight.
Inside the hull are a number of tanks called
ballast tanks which is used to control its position
and depth from the surface of the sea.
If ballast tanks empty ⇒Upthrust = weight ⇒
submarine floats
If ballast tanks full ⇒ Upthrust < weight ⇒
submarine sinks
Determine
(a) The upthrust
(b) The mass of sand in the glass tube.
Solution
3
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
(3) Hydrogen –filled balloon.
The balloon descends when
Upthrust < Weight of hot air (helium gas) +
weight of airship fabric + weight of gondola +
weight of passengers
The balloon remains stationary when
Upthrust = Weight of hot air (helium gas) +
weight of airship fabric + weight of gondola +
weight of passengers
(4) Hydrometer
A hydrogen-filled balloon will float up into the air
if it is released. Air is a fluid and produces an
upthrust.
Density of air >>> density of hydrogen gas
The balloon floats and rises upwards because
Uptrust > Weight of hydrogen + weight of
balloon + weight of string
The balloon remains stationary in air when
Uptrust = Weight of hydrogen + weight of
balloon + weight of string
4)
Hot air balloon
An hydrometer is an instrument used to
measure the density of a liquid.
It has a glass bulb which contains some lead to
make it float upright , and long narrow neck with
a scale marked on it caused the hydrometer
more sensitive.
The large air-filled glass bulb is used to displace
more liquid and it caused the upthrust increases
hence the hydrometer floats.
In a liquid of lesser density , the hydrometer is
more submerged.
The hydrometer floats higher in a liquid of higher
density.
Density of hot air <<< density of cold air
The balloon’s height can be controlled by
turning the gas burner which heats the air on
and off as needed.
The hot air balloon floats and rises upwards
when
Upthrust > Weight of hot air (helium gas) +
weight of airship fabric + weight of gondola +
weight of passengers.
4
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
TUTORIAL 2.5
1
The figure shows a load hung from a spring
balance is slowly submerged in water until it is
immersed completely.
3
The figure shows four spheres , P, Q, R and S
floating on water.
Which comparison is correct about the density
of spheres P,Q,R and S?
A
C
What will happen to the spring balance reading?
A
B
C
D
2
zero
decreases until zero
remains unchanged
decreases until reaches a constant value
4
Which of the following figure is true?
40N
20N
5N
B
D
30N
10N
1.2 N
3.0 N
4.0 N
B
D
2.6 N
3.4 N
An object has a volume 5 x 10- 4 m3 is hung
from a spring balance. The reading of the
spring balance is 8N.If the object is immersed
fully in a liquid with a density 600 kg m-3,
determine the reading of the spring balance
now?
A
C
E
5
S>Q>R>P
Q > R > P >S
An object of mass 2 kg with a density of
8 x 103kgm-3 is immersed in the sea water .If
the density of the sea water is
1.03 x 103 kg m-3, what is the upthrust?
A
C
E
6
B
D
A metal block has a volume 0.002 m3 is
immersed in water. If the density of water is
1000 kgm-3,what is the buoyant force
experienced by the metal block?
A
C
E
5
P>Q>R>S
P>R>Q>S
1N
3N
8N
B
D
2N
5N
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
7
A body has a weight of 20N in air and 15 N in a
liquid. If the volume is 5x 10-4 m3 , what is the
density of the liquid?
A
C
E
8
B
D
800 kgm-3
1200 kgm-3
What is the upthrust of the balloon?
Which of the following about a ship floating on
the surface of sea is true?
A
B
C
D
9
400 kgm-3
1000 kgm-3
1200 kgm-3
A
C
E
The weight of the ship equals to mass of
the sea water displaced
The weight of the ship equals to the weight
of the sea water displaced
The weight of ship is less than the weight
of the sea water displaced
The weight of the ship is more than the
weight of the sea water displaced
11
10 N
100 N
2 000 N
B
D
20 N
200 N
The figure shows a cube of sides 0.1 m floats in
water with ¼ of its height above the water level.
[ The density of water = 1000 kgm-3]
The figure shows a sphere object floating on
the surface of a liquid.
What is the weight of the cube?
A
C
E
Which of the following is true?
A
B
C
D
10
12
The volume of the liquid displaced by the
sphere object equals to the volume of the
sphere object
The weight of the liquid displaced by the
sphere object equals to the weight of the
sphere object
The mass of the sphere object equals to
the mass of liquid in the container
The density of sphere object equals to the
density of the object
2.5N
7.5N
12.5N
B
D
5.0 N
10.0N
The figure shows a boy on a float.
Which of the relationship between the physical
quantities in the above situation is correct?
The figure shows a balloon of mass 200 kg is
floating in a stationary position in the air.
A
B
C
6
Weight of water displaced = weight of the
boy + weight of the float
Weight of water displaced > weight of the
boy + weight of the float
Volume of water displaced = volume of the
boy + volume of the float
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
D
13
Volume of water displaced > volume of the
boy + volume of the float
The figure shows a boat has a safety limit line L.
The volume of the boat under the line L is 4 m3.
The mass of the boat is 200 kg.
[ The density of water = 1000 kgm-3 ]
What is the tension,T of the string?
What is the maximum load can be carried by the
boat to ensure the the boat does not overload?
A
C
E
14
2.0 X 103 Kg
4.0 X 103 Kg
5.0 X 103 Kg
B
D
3.0 x 104 N
4.0 x 104 N
5.0 x 104N
A
C
E
16
3.8 X 103 Kg
4.2 X 103 Kg
17
Submarine
Hot air balloon
B
D
Ship
Aeroplane
(b)
(c)
(a) Compare the readings of the spring
balance in Figure(a) and Figure(b)
What is the mass of the test tube?
0.008 kg
0.016 kg
0.040 Kg
B
D
Figure(a), Figure(b) and Figure(c) show a spring
balance supporting a metal block K in three
situations.
(a)
A
C
E
3.5 x 104N
4.5 x 104N
Which of the following is not the application of
Archimedes’ Principle?
A
C
The figure shows The figure shows a test tube
with uniform diameter and cross-sectional area
2 x 10-4 m2 , and it is filled with sand of mass
0.012 kg so that it is made vertical in a beaker
containing water at a height 0.01 cm
[ Density of water is 1000 kg m-3 ]
B
D
0.012 kg
0.020 kg
………………………………………………
………………………………………………
(b) Name three forces that act on K when it
partially or totally in water.
15 The figure shows a metal block has a volume
0.5 m3 is tied to a string. The block is immersed
in water.
[ Density of the metal block = 8 x 103 kg m-3,
Density of water = 1 x 103 kg m-3]
…………………………………………………
…………………………………………………
(c) State and explain the relationship between
the forces in (b).
………………………………………………
7
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
………………………………………………
(d) Name the principle involved in (c)
…………………………………………………
(a) (i)
(e) (i)
What will happen to the reading
of the spring balance in Figure (c) if
the water is replaced with salt
solution?
………………………………………..
………………………………………
(ii)
………………………………………..
………………………………………
Give one reason for your answer.
………………………………………..
(ii)
………………………………………
18
Based on Figure (a), Figure (b), Figure
and Figure (d), state one observation
common to both the wooden block and
the submarine.
………………………………………
Figure (a) shows a wooden block with load, fully
immersed in water. When the load is
removed, the wooden block floats as shown in
Figure (b).
List the forces which act on the
wooden block and the submarine in
Figure (b) and Figure (d).
…………………………………...
……………………………………
……………………………………
……………………………………
(iii) State the relationship between the
forces listed in (a)(ii).
Figure (c) shows a submarine, immersed in
water with the ballast tanks filled with water.
When the ballast tanks are emptied, the
submarine floats as shown in Figure (4).
…………………………………
…………………………………
(iv) Give one reason for your answer.
………………………………….
…………………………………..
8
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
(b) Name the principle involved in the observations
in Figure(a), Figure (b), Figure (c) and Figure(d).
…...………………………………………
(c) (i) What happens to the block in Figure (b)
when a salt solution is added to the water?
…………………………………………….
…………………………………………….
(ii)
Give one reason for your answer.
………………………………………..
19
What is
(e) The volume of the water displaced by the
block at the new position?
A wooden block has a volume 2 x 10-3m3 and a
density of 900 kgm- 3. Determine
(a) The mass of the wooden block
(f)
The new buoyant force of the block ?
(b) The weight of the wooden block
The wooden block is immersed partially as
shown in Figure (a) and it floats in a stationary
position.
(g) The acceleration of the wooden block if the
force is removed?
20
(a)If the density of helium gas is 0.18 kg m-3,
determine
(i) the mass of the helium gas in the
balloon.
Figure(a)
What is
(c)
A large balloon is made by nylon bag is filled
with 8 m 3 helium gas.
The buoyant force of the block ?
(ii)
(d) The volume of the water displaced by the
block.
[ Density of water = 1000 kg m-3]
The wooden block is later pushed by a force
until the upper surface of the wooden level is
same as the water surface level as shown in
Figure(b) .
9
the weight of the helium gas in
the balloon.
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
(b) The figure shows the ballon later is tied by
a nylon string and a load of mass 3.65
kg hung at the other end of the string.The
balloon floats in a fix height.
[ The density of air =1.25 kg m-3]
………………………………………
………………………………………
………………………………………
………………………………………
………………………………………
21
(a) A fisherman finds that his boat is at
different levels in the sea and in the river,
although the boat carries the same load.
The density of sea water 1 025 kg m-3 and
of river water is 1 000 kg m-3.
Figure(a) and Figure(b) illustrate the
situation of the boat in the sea and in the
river
(i) What is he resultant force acting on
the balloon?
(i)
(ii)
What is meant by density?
Using Figure(a) and Figure(b) ,
compare the levels of the boat and
the volumes of water displaced by
the boat.
Relating the mass of the boat with its
load, the volume of water displaced
and the density of the water , deduce
a relevant physics concept.
(iii)
Name the physics principle that
explains the above situations.
(b) A submarine can sail on the sea surface
and under the sea.
Explain how a submarine on the surface
submerges.
(c) Figure(c) and Figure (d) illustrate the
working principle of a hydrometer. The
depth to which the test tube sinks depends
on its surrounding liquid.
(ii) Calculate the buoyant force acting
on the balloon.
(ii)
(c)
Determine the mass of the nylon bag.
When the string attached to the load
snaps,
(i) What is the acceleration of the
balloon.
(ii)
What will happen to the motion of
balloon when the height of the
balloon increases?
10
S M K Pahi
LESSON 3.5 - Application Archimedes Principal
More difficult to pull the net
Figure(c)
Figure(c)
Figure (a), Figure (b) and Figure (c) show three
different situations when a fisherman is pulling a
fishing net from the sea. In Figure (a), the fisherman
finds it easy to pull a fishing net while most of the net
is in the water. However, the fisherman finds it
difficult as the fishing net is emerging from the
water surface as shown in Figure (b) and Figure (c).
Figure(d)
Explain how you would design a
hydrometer that can determine a wide
range of densities of liquid, using the idea
of the working principle of a hydrometer
shown above.
Draw a diagram that shows the design of
your hydrometer and in your explanation,
emphasize the following aspects:
Based on the observations:
(a) State one suitable inference that can be
made.
(b) State one appropriate hypothesis for an
investigation.
(c) With the use of apparatus such wooden
rod, spring balance,beakerand other
apparatus , describe an experimental
framework to test your hypothesis.
In your description , state clearly the
following:
(i) Aim of the experiment
(ii) Variables in the experiment
(iii) List of apparatus and materials
(iv) Arrangement of the apparatus
(v) The procedure of the experiment
which include the method of
controlling the manipulated variable
and the method of measuring the
responding variable.
(vi) Way you would tabulate the data
(vii) Way you would analysis the data
(i) the stability of the hydrometer
(ii) the sensitivity of the hydrometer
(iii) the ability to measure a wide range of
densities of liquids
(iv) the calibration of the hydrometer
22
Easy topull the fishing net
Figure (a)
Difficult pull the fishing net
Figure(b)
11