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Buoyancy
Name: Alan H.
Status: educator
Age: 20s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
Weights of floating objects
- If you put an object in a tub of water and the object floats, the object
is supported isn't it? So, when you're in a bath for instance you feel
supported.
- Does this mean then, that if you're weighing an object with a
fishing-type scale (ie. one which has its spring pulled downwards by the
object being weighed), and then continue to weigh it once it's being
supported by the water, the measured weight will be less?
- IF this is the case.
- Does this mean that if I add a 200g object to a 2kg tub of water, the
weight (as measured on a scale underneath the tub of water), will be less
than 2.2kg?
I'm sure that can't be the case, but can't really see where the flaw is.
Maybe some confusion re weight/mass. Or re different methods of weighing.
Or perhaps a fish-type-weighing of an object doesn't actually give a lower
weight once it's floating. Or maybe it's something to do with specific
gravity?
Replies:
Alan:
Congratulations on recognizing that a result is flawed, even though you may
not have at your fingertips WHY the answer is unreasonable. The ability to
do such "thought" experiments and predict the anticipated necessary result
is a strategy frequently used by practicing scientists, but difficult to
teach to students --- at any level. Here is the resolution of your paradox:
First, a matter of definitions: strictly speaking, WEIGHT is a force and
MASS is the quantity of matter present. These are related by the equation:
Weight=Mass*g, where 'g' is the acceleration of gravity. This is basically
Newton's Law: Force = Mass x Acceleration. Since 'g' is very nearly the same
everywhere on the earth we use the kilogram both as a unit of Mass and as a
unit of Weight. Not strictly correct, but O.K. for most cases. So if you
have the same object and "weigh" it at various places on the earth, that
same MASS will have different weights, because the acceleration of gravity
varies a little bit from place to place on the earth.
Now to your question: If you have a bucket of water weighing (i.e. with a
mass of) 2 kg weighed in air, and add an object having a mass of 0.2 kg,
also weighed in air, the total mass is 2.2 kg.
Next, take your 0.2 kg object (as weighed in air) and submerge it completely
in the bucket of water. Now, when you weigh the object, it will weigh less
than 0.2 kg. [of course, we assume no overflow etc.] The reason is
Archimedes principle which states that when an object is submerged in a
fluid, the object is buoyed UP by a force numerically equal to the mass of
that volume of fluid displaced by the submerged object. Consequently, the
weight of the object under water is less than its weight in air by an amount
Volume(object) *Density(water).
Weighing an object in and out of a fluid, say water, is a standard method
for determining the mass of objects. It does not depend upon the shape or
geometry of the object.
Even when precisely weighing an object in air, there is a small, but
non-negligible bouncy correction that must be made to account for the volume
of air displaced by the object being weighed. You can find this "bouncy
correction" discussed in most any introductory text on Quantitative
Analysis.
Vince Calder
You intuition is correct, it would weigh 2.2 kg. The concept here is that
of a
closed system. The apparent mass of the object would be less, but the
total mass of
the system as measured from some outside vantage point would be unchanged.
Larry Krengel
Alan,
Let us transfer the concept of "support" to a slightly different picture:
Imagine that you are using a scale to measure the weight of a bag of puppy
chow. You have a big dog, so when the bag is resting fully on the scale
it weighs
50 lbs. Now, you also stand on the scale and the scales read your weight + 50 lbs
because you are both on the scales.
Now you "support" the bag by picking it up. The scales read the same weight as
before (your weight + 50 lbs) because it is supporting the full weight.
Now find a second scale and place it near the first one. Place the puppy chow
on one and stand on the other. Add the two weights and you get your wt +50 lbs.
Reach over and pull up on the bag of puppy chow. The reading of the scale you are
standing on increases while the reading of the other scale decreases but
the TOTAL of the two readings stays the same.
By "supporting" the bag you are simply moving the point of support against
gravity from one location to another. The same is true for things supported by
water. The total weight stays the same.
Greg Bradburn
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