Physics 2015 – Archimedes’ Principle
Minilab 10
Archimedes’ Principle
Department of Physics & Astronomy
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Physics 2015 – Archimedes’ Principle
The purpose of today’s lab is to investigate
Archimedes’ Principle and buoyant forces.
First, we will determine the density of metal
balls of the same substance, but different
radii. Then, once this density is known, we
will use a metal slug (made of the same
metal) to find the buoyant force of 4
different substances.
PURPOSE
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Physics 2015 – Archimedes’ Principle
Activity 1 - Finding Density
• Force sensor (on the stand)
• Beaker with aluminum “basket”
(place the metal balls in here)
• Glass cylinder filled with water
Make sure that you only put water
inside the tall glass cylinders – NO
other liquid goes in here!
EQUIPMENT
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Physics 2015 – Archimedes’ Principle
Activity 2 - Finding Fluid Density
• You will find 4 different plastic containers
full of the following substances:
•
•
•
•
Tap Water
Salt Water
Corn Syrup
Isopropyl Alcohol (70%)
• Attach the metal slug to the end of the
force sensor, and place it into the substances
to see how much force acts on the slug.
EQUIPMENT
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Physics 2015 – Archimedes’ Principle
Archimedes’ Principle is straightforward:
• An object that is submerged in a liquid will
experience an additional upward force equal
to the weight of the amount of liquid that
was displaced by the object. This is called
the buoyant force.
Translated into English, this means:
• Extra force acts on an object when it is
placed in water. This makes the objects
appear lighter than they really are.
THEORY
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Physics 2015 – Archimedes’ Principle
Example
• A metal ball with volume 50 𝑐𝑚2 is placed
completely underwater. It will experience a
buoyant force as shown below:
𝐹𝑏 = 𝑚𝑤 𝑔 = 𝜌𝑤 𝑉𝑔
Translated into English, this means:
• Extra force acts on an object when it is
placed in water. This makes the objects
appear lighter than they really are.
THEORY
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Physics 2015 – Archimedes’ Principle
If we look at the free body diagram, we see:
∑𝑭: 𝑻 − 𝑭𝒃 = 𝑾
As we would learn in a general Physics text,
there are two forces due to
buoyancy, where w = water
and m = mass:
T 𝑭𝒃
𝑭𝒃 = 𝒎𝒘 𝒈 = 𝝆𝒘 𝑽𝒈
𝑾 = 𝒎𝒎 𝒈 = 𝝆𝒎 𝑽𝒈
W
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THEORY
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Physics 2015 – Archimedes’ Principle
Note in the picture that there are no
moving objects, so 𝒂 = 𝟎 → ∑𝑭 = 𝟎
→ 𝑻 + 𝝆𝒘 𝑽𝒈 = 𝝆𝒎 𝑽𝒈
→ 𝑻 = 𝑽𝒈(𝝆𝒎 − 𝝆𝒘 )
In Activity 1, we will use spherical balls:
𝟒 𝟑
𝟒 𝟑
𝑽 = 𝝅𝒓 → 𝑻 = 𝝅𝒓 𝒈(𝝆𝒎 − 𝝆𝒘 )
𝟑
𝟑
In Activity 2, we will use a metal slug:
𝑽 = 𝝅𝒓𝟐 𝒉 → 𝑻 = 𝝅𝒓𝟐 𝒉𝒈(𝝆𝒎 − 𝝆𝒘 )
THEORY
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Physics 2015 – Archimedes’ Principle
There is one more idea you will want to
consider before starting the lab
• Remember to “Tare” your force sensor
before any procedure. In this case, tare
the sensor AFTER YOU PUT THE
BASKET ON THE SENSOR for Activity 1.
This will negate the weight of the basket
on your experiment!
• When you graph this in Excel, you should
expect the line to go through the origin.
Why do you think this is?
THEORY
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Physics 2015 – Archimedes’ Principle
Activity 1
• Using the setup shown on Slide 3, place a
few balls with different radii into the metal
basket, and record the forces displayed in
Capstone.
• You will plot these values with respect to 𝑟 3
to find a mathematical relationship between
the force and the density.
PROCEDURE
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Physics 2015 – Archimedes’ Principle
Activity 2
• Tie the metal slug onto the force sensor,
THEN tare it! (like the left picture)
• You can then place the
Tare
slug into the different
substances (like the
right picture)
PROCEDURE
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Physics 2015 – Archimedes’ Principle
Activity 3
• You will determine the density directly using
the density equation:
𝑀𝑎𝑠𝑠
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑉𝑜𝑙𝑢𝑚𝑒
• This direct calculation will give you a
comparison for your calculated density!
• Note: It will be easiest to measure an empty
plastic container first!
PROCEDURE
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Physics 2015 – Archimedes’ Principle
• DO NOT POUR ANYTHING BUT WATER
down the drain!
• DO NOT POUR ANYTHING BUT WATER
into the tall glass cylinders!
• Clean up anything that spills IMMEDIATELY!
These can damage equipment in the lab!
Use a paper towel or a sponge
• Put the cardboard covers back on the plastic
beakers before you leave.
FINAL REMINDERS
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