BUOYANT FORCE, ARCHIMEDES PRINCIPLE
(1 lab for this chapter)
*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
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PART I: BUOYANCY - introduction
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 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).
1)
hint: the green arrow is the weight, the orange arrow is the buoyant force
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
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.
1) Do you think a cube of aluminum, a cube of iron , a cube of lead will experience the same buoyant force ?
why ? (they have the same volume. they all sink )
2)Let's immerse an object in a liquid and let's hold it in the liquid. Can you predict if the object will rise (to then float on the surface ) or will sink ? just knowing the density of the object and the density of the liquid ?
2 forces act on the object. The buoyant force (Fb) and the weight of the object (W) .
Compare the algebraic expressions of these 2 forces to answer the question.
REmember: mass = density x volume or weight = density x volume
also: volume of water displaced = volume of the object if the object is totally immersed.
Hint: buoyant force = g x (density liquid) x (volume object )
weight object = g x (density object) x (volume object)
3) 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.
4) A cubic decimeter, (V= 1.00 10-3 m3) , of aluminium is submerged in water.
The density of aluminium is d = 2.70 103 kg/m3.
A) What is the magnitude of the buoyant force acting on the metal ?
hint: Fb = 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
5) 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 )
hint: for a given mass, increasing the volume, decreases the density.
buoyancy, gravity and titanic. what happens to a ship when weight is not
balanced by buoyancy.
labpressure : apparent weight
6) A 0.5 kg block of wood is floating in water. WHat is he magntitude 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
7) 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 )
8) 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)
9) A teenager is floating in a freshwater lake with her lake 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 teenater x density water x g solve for the volume)
10) 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
PART I: BUOYANCY - introduction
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 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).
1)
 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 __________ |
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
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.
1) Do you think a cube of aluminum, a cube of iron , a cube of lead will experience the same buoyant force ?
why ? (they have the same volume. they all sink )
2)Let's immerse an object in a liquid and let's hold it in the liquid. Can you predict if the object will rise (to then float on the surface ) or will sink ? just knowing the density of the object and the density of the liquid ?
2 forces act on the object. The buoyant force (Fb) and the weight of the object (W) .
Compare the algebraic expressions of these 2 forces to answer the question.
REmember: mass = density x volume or weight = density x volume
also: volume of water displaced = volume of the object if the object is totally immersed.
Hint: buoyant force = g x (density liquid) x (volume object )
weight object = g x (density object) x (volume object)
3) 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.
4) A cubic decimeter, (V= 1.00 10-3 m3) , of aluminium is submerged in water.
The density of aluminium is d = 2.70 103 kg/m3.
A) What is the magnitude of the buoyant force acting on the metal ?
hint: Fb = 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
5) 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 )
hint: for a given mass, increasing the volume, decreases the density.
buoyancy, gravity and titanic. what happens to a ship when weight is not
balanced by buoyancy.
labpressure : apparent weight
6) A 0.5 kg block of wood is floating in water. WHat is he magntitude 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
7) 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 )
8) 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)
9) A teenager is floating in a freshwater lake with her lake 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 teenater x density water x g solve for the volume)
10) 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