LECTURE 3
BUOYANCY (ARCHIMEDES’ PRINCIPLE)
Lecture Instructor: Kazumi Tolich
Lecture 3
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Reading chapter 15.4 and 15.5
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Archimedes’ principle and buoyancy
Buoyancy and Archimedes’ principle
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The force exerted by a fluid on a body wholly or partially submerged in it is called
the buoyant force.
Archimedes’ principle:
An object completely immersed in a fluid experiences an upward buoyant force
equal in magnitude to the weight of fluid displaced by the object.
𝐹" = 𝜌%&'() 𝑔𝑉
𝑉 is the volume of displaced fluid by the object.
Demo: 1
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Archimedes’ principle
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The buoyant force is equal to the weight of the water
displaced.
Quiz: 1
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Suppose that a rock is sitting on a chair, both
submerged in water. Another identical rock is sitting
on a chair in the air. Which chair exerts greater
normal force on the rock?
A.
B.
C.
The chair in the water
The chair in the air
Actually, both chairs exert the same amount of force.
Quiz: 3-1 answer
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A.
The chair in the air
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The rock is sitting, so it is not accelerating. The net force on it is zero.
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The rock has the following forces: buoyant force by the fluid (upward),
normal force by the chair (upward), and weight (downward)
𝐍/6
The weight of the rocks are the same since they are identical.
The buoyant force by the air is smaller because air is less dense while
the volume of the rocks are identical:
𝐹", .(/ = 𝜌.(/ 𝑔𝑉 < 𝐹", 1.23/ = 𝜌1.3/ 𝑔𝑉.
This is why it is easier to lift a rock (or any object) in water than in air.
𝐁/% 𝐖/8
The crown and the nugget
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Archimedes (287-212 BC) had been given the task of determining whether a crown
made for King Hieron II was pure gold.
In the above diagram, crown and nugget balance in air, but not in water because the
crown has a lower density.
Quiz: 2
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An inverted glass jar, filled with air, sits on a table. A helium
balloon inside the jar floats to the top. If the air is replaced
with helium, what will happen to the helium balloon?
A.
it still floats at the top because it has a upward buoyant force.
B.
it stays in the middle because it has zero net force.
C.
it sinks to the bottom because of the weight of the balloon.
D.
the balloon shrinks in size due to the surrounding helium.
E.
the balloon grows in size due to the lack of surrounding air.
Quiz: 3-2 answer
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it sinks to the bottom because of the weight of the balloon.
The balloon floats initially because the displaced air weighs more than the
balloon, so the buoyant force provides a net upward force.
When the balloon is in the lighter helium gas (instead of air), the displaced
helium gas provides a buoyant force equal to the weight of the gas in the
balloon.
But it does not provide enough upward buoyant force to support the weight
of the balloon.
Quiz: 3
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Now the jar is lifted off the table, but the jar remains inverted
to keep the helium gas in the jar. What will happen to the
balloon?
A.
It floats at the top of the jar.
B.
It floats so that the bottom of the balloon is near the bottom of the jar.
C.
It floats so that the top of the balloon is near the bottom of the jar.
D.
It sinks down to the surface of the table.
Quiz: 3-3 answer
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It floats so that the bottom of the balloon is near the bottom of
the jar.
The balloon sinks in the helium gas until it hits the surface of the
air.
Because the balloon floats in air, it will float on the surface of
the air and therefore remain mostly inside the jar, but at the
bottom.
Demo: 2
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Helium balloon in helium
Helium balloon in liquid nitrogen
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Demonstration of buoyancy and Archimedes’ principle
Example: 1
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A block of an unknown
material’s apparent
weight is 𝑊. = 5.00 N
in air and 𝑊1 = 4.55 N
when submerged in
water. What is the
density of the material?
Quiz: 4
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A.
B.
C.
D.
Which of the following statements is/are correct? Choose all that apply.
For an object to float in water, its density must be less than that of water.
For an object to float in water, its density must be more than that of
water.
For an object to float, it must displace water whose volume is the same as
the volume of the object.
For an object to float, it must displace water whose weight is the same as
the weight of the object.
Quiz: 3-4 answer
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For an object to float, it must displace water whose weight is the same as the weight of the object.
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For an object to float, the net force on it must be zero since it is not accelerating vertically.
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The the magnitude of the buoyant force must be equal to the magnitude of the weight.
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𝐹" = 𝜌%&'() 𝑔𝑉, where 𝑉 is the volume of displaced fluid by the object.
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An object that is denser than fluid can float if it displaces enough fluid because of its shape.
Demo: 3
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Battleship
Board and weights
Quiz: 5
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Two beakers, a and b, are filled to the brim with
water. A wooden block is placed in beaker b so that
it floats. (Some of the water will overflow the
beaker). Both beakers are then weighed. Which
scale reads a larger weight?
Quiz: 3-5 answer
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Same for both
Since the wooden block floats, the net force on the block is
zero.
The wooden block displaces an amount of water whose weight
is the same as the weight of the block.
Example: 2
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What is the minimum area of
the top surface of a slab of ice
with thickness, ℎ = 0.30 m,
floating on fresh water that will
hold up an automobile of mass
𝑚6 = 1100 kg sitting on top?
The density of water and ice
are 𝜌1 = 0.998 × 10B kg/m3
and 𝜌( = 0.917 × 10B kg/m3,
respectively.