Grades 4-7
How Much Do You Weigh
Archimedes’ Principle and How Things Float
WHAT YOU NEED
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Large Cardboard Box: Big enough
for you to fit in.
Ball-Pit Balls: Enough to fill the box.
You can also use foam peanuts.
Bathroom Scale
10 Quart Bucket: A bucket this size
holds about 12 lbs. of water.
Swimming Pool Floatie: The kind
that goes around your waist.
Your Body
WHAT TO DO
Meets KY Education Standards:
SC-E-1.1.1, SC-E-1.1.2, SC-M-1.1.1
Step 1:
Use the bathroom
scale to find your weight in air.
Get into the box and fill it with
ball-pit balls. Get out of the box.
Add balls to the box one bucket
at a time until it’s full again.
Count how many buckets you
need to fill the box again.
Step 2:
Put on the floatie and weigh yourself with
the floatie.
Get into the box while wearing the floatie. Fill the box
with ball-pit balls, then get out of the box. Count how
many buckets of balls you need to fill the box again.
Under Water?
Step 3:
Multiply the number
of buckets needed to fill the box
the first time by 12 lbs. per
bucket. Subtract this number
from your weight in air. This is
how much you weigh under water.
Do the same computation for
when you wore the floatie. This
is how much you weigh under
water while wearing a floatie.
Meets KY Education Standards:
SC-E-1.1.1, SC-E-1.1.2, SC-M-1.1.1
WHAT’S
GOING ON?
The famous mathematician Archimedes of Syracuse (287-212 B.C.) discovered the principle of
buoyancy, or why things float. After his discovery while taking a bath, Archimedes is rumored
to have run naked through the streets shouting “Eureka! I’ve found it!”
Archimedes’ Principle is stated as follows: “To determine the weight of an object in a fluid, you
subtract from the weight of the object in air the weight of the fluid displaced by the object.” This
principle is actually very easy to understand: Gravity is a force that pulls down on your body.
When you get in a swimming pool not only does gravity pull down on your body, but the water
pushes upward. Your weight under water is the force of gravity pulling down, in other words
your normal weight in air, minus the force of the water pushing up.
How hard does the water push up? You can find this out easily. Suppose that the box you
climbed into was initially filled with water. If you got in, some of the water would come out of
the box. We say that your body displaces some of the water. How much water does your body
displace? This depends on your size. You figured out how many buckets of water take up the
same amount of space as your body. More importantly, you also figured out how heavy that
much water is. In other words, you found out how much you would weigh if you opened up
your skin, took out all your organs and filled your skin up with water. Remarkably, the strength
of the force that the water exerts upward on your body equals the weight of the water displaced
by your body.
You can use Archimedes’ Principle to determine if an object sinks or floats. If the object
weighs more than the water that it displaces, gravity pulls down more than the water pushes
up. The object sinks. If the object weighs less than the water that it displaces, gravity pulls
down less than the water pushes up. The object floats. By putting on the floatie, you increase
the amount that gravity pulls down on your body by only a small amount. But, since the floatie
is large, it makes your body displace a larger amount of water and increases the force that the
water exerts upward. A large steel ship can float even though a small coin sinks because the
boat displaces an amount of water that weighs more than the boat. That’s a lot of water!
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WHAT TO NOTICE
While not wearing the floatie your body
weighs more than the amount of water that
takes up the same amount of space as your
body. Therefore, your weight under water is
positive and you’ll sink.
When you put the floatie on you added only
about one pound to your weight in air. But,
you significantly increased the volume of
your body (including the size of the floatie).
You needed to add several more buckets to
the box when your wore the floatie.
While wearing the floatie, your body weighs
less than the amount of water that takes up
the same amount of space as your body and
the floatie. Therefore, your weight under
water while wearing a floatie is negative.
This means you weigh less than 0 lbs. under
water. You’ll float!