BUOYANT FORCE, ARCHIMEDES PRINCIPLE
*Archimedes was asked by Hiero II, his king, to determine whether a crown was pure gold or was alloyed with silver. Archimedes was perplexed, until one day, observing the overflow of water in his bath, he suddenly realized that since gold is more dense (i.e., has more weight per volume) than silver, a given weight of gold represents a smaller volume than an equal weight of silver and that a given weight of gold would therefore displace less water than an equal weight of silver. Delighted at his discovery, he ran home without his clothes, shouting "Eureka, which means "I have found it. He found that Hiero's crown displaced more water than an equal weight of gold, thus showing that the crown had been alloyed with silver (or another metal less dense than gold). UTUBE video to tell you the story
source
LAB1:apparent weight
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PART I: BUOYANCY - introduction
0)READ
In the previous chapter we saw that the excess pressure in a liquid due to its weight is given by:
P = h d g
h is the height of the reservoir , d is density of the liquid and g the acceleration due to gravity (10m/s/s about).
If an object takes some volume in a liquid, it will not withstand the same pressure on its top than on its bottom.
In a liquid, there is more pressure on the top area than on the bottom area.
This is because of P = h d g. as h increases , the pressure increases too.
Note that the pressure exerted on one side is balanced by the pressure exerted on the opposite side.
The total force is therefore upward and is called the buoyant force.
By comparing this buoyant force to the weight of the object , you will know if the object will sink or rise (and float).
source image: http://sol.sci.uop.edu/~jfalward/physics17/chapter5/chapter5.html
1) FILL THE BLANKS
hint: the green arrow is the weight, the orange arrow is the buoyant force
EXTRA CREDITS:
I Want To Make Something!: How To Make A Submarine
2) READ
Let's compute the buoyant force. Suppose the object has a height = l
On the top area, the downward force is Ftop = Ph x area with Ph = d g h
On the bottom area the upward force is Fbottom = Ph+l x area with Ph+l = d g (h+l)
So the net force is Fnet = F buoyant = Fbottom - Ftop = d g l x area
F buoyant = (density of water) x g x (height of object) x (area of object)
or F buoyant = (density of water) x g x (volume of object)
0r F buoyant = (mass of water displaced) x g REMEMBER THE TRIANGLE ? m = d x V
The magnitude of the the buoyant force is equal to the weight of the fluid displaced by the object.
This relationship was discovered by Archimedes 212 BC.
An object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
Buoyancy is the ability of a fluid to exert an upward force on an object place in it. Buoyancy results in the apparent loss of weight
of an object in a fluid.
WATCH THIS VIDEO, nice review of density.
2 forces act on an object in a liquid: its weight and the buoyant force. They compete with each other.
If weight of the object is greater than the buoyant force, the object sinks.
Suppose the object is totally immerged and sinks , this means buoyant force wins:
weight object = mass x g = density object x volume object x g
buoyant force = weight of volume water displaced = mass of water displaced x g = density water x volume object x g
SO buoyant force < weight object if density water < density object
AN OBJECT SINKS IF ITS DENSITY IS GREATER THAN WATER's = 1g/cm3
3) Do you think a cube of aluminum, a cube of iron , a cube of lead will experience the same buoyant force ?
why ?
hint: they have the same volume. they all sink
4) A)The _________ is the net upward force exerted by a fluid on a submerged or immersed object.
B) Match each sentence with the correct result.
4) A)How much liquid does a completely submerged object displace?
B) Describe a method of determining the volume of an irregularly shaped object.
C) What does Archimedes ' principle state ?
D) What does immersed mean ?
5) A) A submerged object's _____________ determines the buoyant force.
B) When the buoyant force equals the weight of an object completely submerged in water, then the object's weight must equal______________________
6) Match each phrase with the correct word or words.
7) Why does a submarine take in or release water from its ballast tanks ?
So a submarine changes its ___________ not its volume.
8) How do fish control their density? (google)
So a fish changes its __________ not its weight. It changes the _______ force, not the weight
9) Every ship must be designed to displace a weight of water equal to ___________________________
10) For an object to float, its density has to be smaller than the density of water.
A huge steel boat will float . Can you explain why ? (density = mass/volume)
11) Explain how a hot ballon can rise, using Archimede's principle. (a hot balloon is filled with hot air and rises
in cold air).
12) Can a hot balloon rise in space ? (no air around to push away)
buoyancy, gravity and titanic. what happens to a ship when weight is not
balanced by buoyancy.
labpressure : apparent weight
ANIMATION:
http://www.mhhe.com/physsci/physical/giambattista/fluids/fluids.html
PART II PROBLEMS
1) A cubic decimeter of steel is submerged in water. (density of water = 1000kg/m3)
A) What is the magnitude of the buoyant force acting on the steel ? side = 1 dm = 0.1m and g= 10m/s/s
hint: volume = side3 . Fb = g x density x volume
B) What is the weight of the cube ? (density of steel = 9000kg/m3 )
hint: weight = volume x g x density /
C) Immersed in the liquid, the cube will rise or sink? why ?
D) The weight of the object is larger than the buoyant force. Find the net downward force acting on the object.
hint: Fnet = larger force - smaller force or weight - Fb
E) If you were to weigh (N) the object while still immersed. What do you expect to find ?
this is called the apparent weight. This is why an object seems lighter when carried in water.
2) A cubic decimeter, (V= 1.00 10-3 m3) , of aluminum is submerged in water.
The density of aluminum is d = 2.70 103 kg/m3.
A) What is the magnitude of the buoyant force acting on the metal ?
hint: Fib = density water x volume object immersed x g
B) immersed in water, the cube will rise or sink ?
C) What is the apparent weight of the block ?
hint: apparent weight = weight - buoyant force
3) A 0.5 kg block of wood is floating in water. WHat is he magnitude of the buoyant force acting on the block ?
hint: the wood floats. That means the buoyant force is balanced by the weight of the block
4) A certain boat displaces a volume of 2.5 m3 of water.
(the density of water is 1000kg/m3)
A) What is the mass of the water displaced by the boat ?
(hint: mass = (density of water ) x volume displaced )
B) What is the buoyant force acting on the boat ?
(hint: buoyant force = weight of water displaced = mass of water displaced x g )
5) A rock with a volume of 0.2 m3 is fully submerged in water having a density of 1000 kg/m3.
What is the buoyant force acting o the rock ?
(hint: buoyant force = weight of water displaced = mass of water displaced x g = volume displaced x density water x g = volume rock x density water x g)
6) A teenager is floating in a freshwater lake with her head just above the water. If she weighs W = 600N, What is her volume?
(in m3, density water = 1000kg/m3)
(hints: she is floating. The weight is balanced by the buoyant force = W = weight of water displaced = volume of teenager x density water x g solve for the volume)
7) What is the tension in a wire supporting a 1250N camera submerged in water ?
The volume of the camera is 8.3 10-2 m3.
hint1: tension in the wire = apparent weight of the camera in water = weight in air (1250N) - buoyant force.
You need to find the buoyant force.
hint2: buoyant force = weight of water displaced = volume of water displaced x density of water x g = volume of camera x density water x g
8) An iceberg has a volume V = 3 105 m3. An iceberg is made of ice with air bubbles trapped inside.
The density of an iceberg is about 826kg/m3. So the mass of 1m3 of iceberg is ____________.
We know that 4/5 of an iceberg is under water. (submerged)
A) Find the weight of the iceberg. (force of gravity). use g = 10m/s/s.
B) The iceberg floats. The 2 forces acting on it have to balance each other.
What are these forces ?
C) Draw an floating iceberg and draw the 2 forces acting on it. Make sure that 4/5 of the iceberg
is under the water. use graph paper.
(for example draw, the outline of the iceberg by outlining 25 little squares o the graph paper.
Pick 5 top squares to be above water . (25/5) and 20 to be below water )
D) Find the buoyant force ?
(the forces are balanced. down force = up force)
E) the volume of the icebergy is given. ( V = 3 105 m3 ). Find the volume of water displaced.
hint: volume of water displaced = volume of iceberg immersed = 4/5 V
F) using D) and E) , Find the density if the sea water.
Fib = density water x volume object immersed x g
9) An hot air balloon displaces a volume of 700m3 of air. The mass of the balloon including cords
and basket is 350kg. The load can be as much as 450kg (in addition to the 350kg).
A) Find the buoyant force acting on the balloon if 1 m3 of air weighs 13N.
hint: Fb= weight of displaced air = weight of 700m3
B) What is the mass that the balloon can lift ?
hint: buoyant force = load in equilibrum and load = mass x 10
10) What are the 2 forces acting on a hot balloon ?
Instead of using hot air (less dense than cold ) air you can also use a gas like hydrogen
or helium. What is the problem with hydrogen ? Tell the stoy of the Zeplin hindenburg.
LZ129 Hindenburg
11) A) Use internet/encyclopedia to find the density of the gas hydrogen = ________ kg/m3
Compare to density of air (1.3 kg/m3)
hint: divide density of air by density of hydrogen. (ratio)
The density of air is about ___________ times the density of air
B) Same question for helium = ___________ kg/m3
so density of air is __________ times density of helium
C) same question for hot air = ____________kg/m3
12) The lift from a air balloon or an hot air balloon is equal to the volume displaced.
Air is 1000 times less dense than water. so 1 kg take 1000 L of space (or 1 cubic meter).
That means you need 1 cubic meter of helium in a balloon to lift 1 kg.
If a child is 50 kg and wants to fly with a helium balloon, he needs a balloon filled
with _______ cubic meters of helium.
To lift 100kg of material, the ballon needs a volume of _______- cubic meters. This is how big are
the hot air balloon are.
PART I: BUOYANCY - introduction
0)READ
In the previous chapter we saw that the excess pressure in a liquid due to its weight is given by:
P = h d g
h is the height of the reservoir , d is density of the liquid and g the acceleration due to gravity (10m/s/s about).
If an object takes some volume in a liquid, it will not withstand the same pressure on its top than on its bottom.
In a liquid, there is more pressure on the top area than on the bottom area.
This is because of P = h d g. as h increases , the pressure increases too.
Note that the pressure exerted on one side is balanced by the pressure exerted on the opposite side.
The total force is therefore upward and is called the buoyant force.By comparing this buoyant force to the weight of the object , you will know if the object will sink or rise (and float).
source image: http://sol.sci.uop.edu/~jfalward/physics17/chapter5/chapter5.html1) FILL THE BLANKS
 Placed in water, this object will _____________. the ______ is larger than __________________ |  Placed in water, this object will not ______ . The ______ balances the ___________________. |  Placed in water this object will _____. The _______ is larger than the __________ |
EXTRA CREDITS:
I Want To Make Something!: How To Make A Submarine
2) READ
Let's compute the buoyant force. Suppose the object has a height = l
On the top area, the downward force is Ftop = Ph x area with Ph = d g h
On the bottom area the upward force is Fbottom = Ph+l x area with Ph+l = d g (h+l)
So the net force is Fnet = F buoyant = Fbottom - Ftop = d g l x area
F buoyant = (density of water) x g x (height of object) x (area of object)
or F buoyant = (density of water) x g x (volume of object)
0r F buoyant = (mass of water displaced) x g REMEMBER THE TRIANGLE ? m = d x V
or F buoyant = (weight of water displaced)
The magnitude of the the buoyant force is equal to the weight of the fluid displaced by the object.
This relationship was discovered by Archimedes 212 BC.
An object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
Buoyancy is the ability of a fluid to exert an upward force on an object place in it. Buoyancy results in the apparent loss of weight
of an object in a fluid.
WATCH THIS VIDEO, nice review of density.
2 forces act on an object in a liquid: its weight and the buoyant force. They compete with each other.
If weight of the object is greater than the buoyant force, the object sinks.
Suppose the object is totally immerged and sinks , this means buoyant force wins:
weight object = mass x g = density object x volume object x g
buoyant force = weight of volume water displaced = mass of water displaced x g = density water x volume object x g
SO buoyant force < weight object if density water < density object
AN OBJECT SINKS IF ITS DENSITY IS GREATER THAN WATER's = 1g/cm3
3) Do you think a cube of aluminum, a cube of iron , a cube of lead will experience the same buoyant force ?
why ?
hint: they have the same volume. they all sink
4) A)The _________ is the net upward force exerted by a fluid on a submerged or immersed object.
B) Match each sentence with the correct result.
| The weight of a submerged object is greater that the buoyant force. | The object will remain at any level |
| The weight of a submerged object is less than the buoyant force. | The object will sink. |
| The weight of a submerged object is equal to the buoyant force. | The object will float on the surface. |
4) A)How much liquid does a completely submerged object displace?
B) Describe a method of determining the volume of an irregularly shaped object.
C) What does Archimedes ' principle state ?
D) What does immersed mean ?
5) A) A submerged object's _____________ determines the buoyant force.
B) When the buoyant force equals the weight of an object completely submerged in water, then the object's weight must equal______________________
6) Match each phrase with the correct word or words.
| An object will sink | AN object has a density equal to the density of the fluid in which it is immersed. |
| An object will float. | An object is more dense than the fluid in which it is immersed. |
| An object neither sinks nor float. | An object is less dense that the fluid in which it is immersed. |
7) Why does a submarine take in or release water from its ballast tanks ?
So a submarine changes its ___________ not its volume.
8) How do fish control their density? (google)
So a fish changes its __________ not its weight. It changes the _______ force, not the weight
9) Every ship must be designed to displace a weight of water equal to ___________________________
10) For an object to float, its density has to be smaller than the density of water.
A huge steel boat will float . Can you explain why ? (density = mass/volume)
11) Explain how a hot ballon can rise, using Archimede's principle. (a hot balloon is filled with hot air and rises
in cold air).
12) Can a hot balloon rise in space ? (no air around to push away)
buoyancy, gravity and titanic. what happens to a ship when weight is not
balanced by buoyancy.
labpressure : apparent weight
ANIMATION:
http://www.mhhe.com/physsci/physical/giambattista/fluids/fluids.html
PART II PROBLEMS
1) A cubic decimeter of steel is submerged in water. (density of water = 1000kg/m3)
A) What is the magnitude of the buoyant force acting on the steel ? side = 1 dm = 0.1m and g= 10m/s/s
hint: volume = side3 . Fb = g x density x volume
B) What is the weight of the cube ? (density of steel = 9000kg/m3 )
hint: weight = volume x g x density /
C) Immersed in the liquid, the cube will rise or sink? why ?
D) The weight of the object is larger than the buoyant force. Find the net downward force acting on the object.
hint: Fnet = larger force - smaller force or weight - Fb
E) If you were to weigh (N) the object while still immersed. What do you expect to find ?
this is called the apparent weight. This is why an object seems lighter when carried in water.
2) A cubic decimeter, (V= 1.00 10-3 m3) , of aluminum is submerged in water.
The density of aluminum is d = 2.70 103 kg/m3.
A) What is the magnitude of the buoyant force acting on the metal ?
hint: Fib = density water x volume object immersed x g
B) immersed in water, the cube will rise or sink ?
C) What is the apparent weight of the block ?
hint: apparent weight = weight - buoyant force
3) A 0.5 kg block of wood is floating in water. WHat is he magnitude of the buoyant force acting on the block ?
hint: the wood floats. That means the buoyant force is balanced by the weight of the block
4) A certain boat displaces a volume of 2.5 m3 of water.
(the density of water is 1000kg/m3)
A) What is the mass of the water displaced by the boat ?
(hint: mass = (density of water ) x volume displaced )
B) What is the buoyant force acting on the boat ?
(hint: buoyant force = weight of water displaced = mass of water displaced x g )
5) A rock with a volume of 0.2 m3 is fully submerged in water having a density of 1000 kg/m3.
What is the buoyant force acting o the rock ?
(hint: buoyant force = weight of water displaced = mass of water displaced x g = volume displaced x density water x g = volume rock x density water x g)
6) A teenager is floating in a freshwater lake with her head just above the water. If she weighs W = 600N, What is her volume?
(in m3, density water = 1000kg/m3)
(hints: she is floating. The weight is balanced by the buoyant force = W = weight of water displaced = volume of teenager x density water x g solve for the volume)
7) What is the tension in a wire supporting a 1250N camera submerged in water ?
The volume of the camera is 8.3 10-2 m3.
hint1: tension in the wire = apparent weight of the camera in water = weight in air (1250N) - buoyant force.
You need to find the buoyant force.
hint2: buoyant force = weight of water displaced = volume of water displaced x density of water x g = volume of camera x density water x g
8) An iceberg has a volume V = 3 105 m3. An iceberg is made of ice with air bubbles trapped inside.
The density of an iceberg is about 826kg/m3. So the mass of 1m3 of iceberg is ____________.
We know that 4/5 of an iceberg is under water. (submerged)
A) Find the weight of the iceberg. (force of gravity). use g = 10m/s/s.
B) The iceberg floats. The 2 forces acting on it have to balance each other.
What are these forces ?
C) Draw an floating iceberg and draw the 2 forces acting on it. Make sure that 4/5 of the iceberg
is under the water. use graph paper.
(for example draw, the outline of the iceberg by outlining 25 little squares o the graph paper.
Pick 5 top squares to be above water . (25/5) and 20 to be below water )
D) Find the buoyant force ?
(the forces are balanced. down force = up force)
E) the volume of the icebergy is given. ( V = 3 105 m3 ). Find the volume of water displaced.
hint: volume of water displaced = volume of iceberg immersed = 4/5 V
F) using D) and E) , Find the density if the sea water.
Fib = density water x volume object immersed x g
9) An hot air balloon displaces a volume of 700m3 of air. The mass of the balloon including cords
and basket is 350kg. The load can be as much as 450kg (in addition to the 350kg).
A) Find the buoyant force acting on the balloon if 1 m3 of air weighs 13N.
hint: Fb= weight of displaced air = weight of 700m3
B) What is the mass that the balloon can lift ?
hint: buoyant force = load in equilibrum and load = mass x 10
10) What are the 2 forces acting on a hot balloon ?
Instead of using hot air (less dense than cold ) air you can also use a gas like hydrogen
or helium. What is the problem with hydrogen ? Tell the stoy of the Zeplin hindenburg.
LZ129 Hindenburg 11) A) Use internet/encyclopedia to find the density of the gas hydrogen = ________ kg/m3
Compare to density of air (1.3 kg/m3)
hint: divide density of air by density of hydrogen. (ratio)
The density of air is about ___________ times the density of air
B) Same question for helium = ___________ kg/m3
so density of air is __________ times density of helium
C) same question for hot air = ____________kg/m3
12) The lift from a air balloon or an hot air balloon is equal to the volume displaced.
Air is 1000 times less dense than water. so 1 kg take 1000 L of space (or 1 cubic meter).
That means you need 1 cubic meter of helium in a balloon to lift 1 kg.
If a child is 50 kg and wants to fly with a helium balloon, he needs a balloon filled
with _______ cubic meters of helium.
To lift 100kg of material, the ballon needs a volume of _______- cubic meters. This is how big are
the hot air balloon are.