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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? Any ideas?


Replies:
Alan,

What you are forgetting is Newton's third law: For every force, there is an equal-sized but opposite reaction force. When the water pushes up on the fish, the fish also pushes down on the water with the same force. Any change to the weight of the tub, water, and fish due to the water pushing up on the fish is balanced by the fish pushing down on the water. The total force needed to support tub, water, AND fish together remains the same.

Dr. Ken Mellendorf


Nope. The object plus the tub of water still has a mass of 2000g + 200g. Just as if you had rested the object on a 2kg block of wood.

I'm sure that can't be the case, but can't really see where the flaw is. Maybe some confusion re weight/mass.

That's part of it. The object immersed in water while hanging from the fish scale still has a mass of 200g (say), part of which is supported by the water and the rest of which is supported by the fish scale. If you weigh the water while you dunk the object, you will find that its weight increases, too, but not by the full 200g. (OK, weight is a force, not a mass, so it's strictly not expressible in units of g, but you know what I mean.) The shortfall, of course, will be the weight supported by the fish scale. If you drop the object and let it sink to the bottom of the bucket, THEN the bucket + water + object will have a "weight" of 2200g. Or re different methods of weighing.

Weighing by a spring tells the force pulling an object toward earth. It is determined by allowing the spring to fully resist the gravitational force (that is, to keep the object from falling), and seeing how much force the spring had to apply to do that. If something besides the spring also pushes up on the object, obviously the spring won't record the full weight of the object Or perhaps a fish-type-weighing of an object doesn't actually give a lower weight once it's floating.

This is easy to test. Does it or doesn't it? I say it WILL record a lower weight.

Or maybe it's something to do with specific gravity?

Not really. If the object has a larger specific gravity than the water, it will sink and the fish scale will record a weight lower than the full weight of the object. If the object has a smaller specific gravity than water, it will float and the fish scale will record a weight of zero. It's just a matter of what fraction of the total is supported by the water.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


Yes. The water is not supplying all of the force required to keep the 200 g object from falling. (If it were, your scale would measure zero.) The scale underneath the tub just has to support the tub, the water, and the force the water exerts on the suspended object. 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?

All you have to do is keep track of the forces: what is exerting what force on what object. (You know from the start that the total force on each object is zero, otherwise it would start moving.)

Tim Mooney



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