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Archemedes' Principal and Weight
Name: Phyllis
Status: other
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
Which weighs more: a 100 pound rock on dry land
or a 100 pound rock totally submerged in water?
Replies:
The 100 pound rock submerged in water weighs less. By Archimedes'
Principal it weighs less by an amount equal to the volume of water
displaced by the volume of the rock.
Vince Calder
Hi Phyllis,
Weight is relative. Let me explain. Mass in the English system is measured
in slugs. (Do not ask me, it is weird, but it is a fun unit.) A 100 pound
rock has a mass of about 3.125 slugs. Mass does not change, so mass of the
rock under the water is the same as above water. A rock, is a rock is a
rock so to speak.
Now weight is another matter, weight = mass times gravity. So technically
rock on Earth, under water on beach approximately =, same same. Mass is
constant; weight depends on where you are in the universe. We use weight and
mass almost interchangeably on Earth because most of us are not going
anywhere soon. So I will just say weight to keep things in layman's terms.
However, you are probably referring to that apparent weight loss we feel
when something is being buoyed up by the water. That depends on the VOLUME
of the rock. As the rock slips under water it displaces an amount of water
equal to its volume. This water has weight. So the amount of water pushed
out of the way by the water pushes back on the rock providing it with a
buoyant force. How much? The force is equal to the weight of water
displaced.
Are you confused yet?
Think of it this way. You probably can not pick up another adult human
being with one hand. Yet you can easily support that adult human being on
his or her back in the water. Why? Because the water that the person's
body pushes out of the way to get under the water is pushing back on the
person and helps hold them up.
So as far as your rock goes, underwater will seem to weigh less. This will
be determined by the size and shape of the rock. If it is a small, compact
100 lb. boulder, it may seem to weigh more underwater than a 100 lb. slab of
a rock that may have a bigger volume to start with.
Hope this helps!
Martha Croll
Dear Phyllis,
If you tie a rope around a 100 pound rock, attach a spring scale to
the end of the rope, and then slowly lower the rock into water, you
will see that the reading on the scale decreases by a large amount
as the rock sinks into the water.
This is because the water (as Archimedes deduced in ancient Grecian
times) exerts an upward (buoyant) force on the rock equal to the
weight of the water which is displaced by the rock. This is easy to
prove, since the water which was displaced by the rock has the
weight of that buoyant force and was exactly supported by the
surrounding water.
Next summer try lifting a large rock in air and then lift it when it
is underwater and I think you will easily detect the difference.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Update: June 2012
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