# how much does a full bath of water weigh?

2

#### 2scoops0406

And if you really want to waste a few brain cells, our favourite mad scientist puts a half-filled glass of water on the scales. He then dips his finger in it without touching any part of the glass (Don't ask why). Do the scales read more, less or the same?

Same.

same

Are you sure?

#### JohnD

more

by the weight of the volume of liquid that he has displaced with his prodder

#### Softus

You don't need to add the weight of the bather to the weight of water.

The bather will displace his own weight of water
No you won't you will displace your own volume of water.
You're both wrong.

Ignoring, for now, the scenario of the bath overflowing, the volume of water displaced by a buoyant object has the same weight as the object. The bath is then supporting the weight of the water and the weight of the floating object.

#### JohnD

... if the bath is filled to the overflow, and you get in, you will displace water which will go down the overflow or slop over the side....

...Ignoring, for now, the scenario of the bath overflowing,...

2

#### 2scoops0406

You don't need to add the weight of the bather to the weight of water.

The bather will displace his own weight of water
No you won't you will displace your own volume of water.
You're both wrong.

Ignoring, for now, the scenario of the bath overflowing, the volume of water displaced by a buoyant object has the same weight as the object. The bath is then supporting the weight of the water and the weight of the floating object.

Ignoring, for now, the scenario of the bath overflowing
Wrong, how can it not overflow? the bath is full.[/quote]

2

#### 2scoops0406

more

by the weight of the volume of liquid that he has displaced with his prodder

Wrong, indeed if the glass was full, and the resulting water displaced ran off the scales then the weight would go down.

The fact that you have stuck you digit into a glass of water, has no effect as there is no additional force exerted onto the scales. weight of course being mass x acceleration. (there is no acceleration unless you cut you finger off).

You could do the same with an olympic swimming pool and a 1000 tonne weight suspended from a crane, there would be no increase in weight of the swimming pool. (as long as the crane is not in the pool!)

2

#### 2scoops0406

the volume of water displaced by a buoyant object has the same weight as the object.

Not true as the object would then be neither buoyant or non-bouyant.

I think this explains it.

#### Kes

more

by the weight of the volume of liquid that he has displaced with his prodder

Wrong, indeed if the glass was full, and the resulting water displaced ran off the scales then the weight would go down.
The question clearly stated a half-filled glass, and the finger not touching the glass. So, discounting a hugely fat finger, the glass cannot overflow.

The fact that you have stuck you digit into a glass of water, has no effect as there is no additional force exerted onto the scales. weight of course being mass x acceleration. (there is no acceleration unless you cut you finger off).
There will always be gravitational pull.

You could do the same with an olympic swimming pool and a 1000 tonne weight suspended from a crane, there would be no increase in weight of the swimming pool. (as long as the crane is not in the pool!)
So, if you had some sort of strain gauge on the crane, it would not change as the weight was lowered into the water? What if your 1000 t weight was the same density as water? What if your 1000 t weight was a boat?

#### Kes

the volume of water displaced by a buoyant object has the same weight as the object.
Should it not be 'the volume of water displaced by any object has the same weight as the object', irrespective of whether the object floats or sinks?

2

#### 2scoops0406

The question clearly stated a half-filled glass, and the finger not touching the glass. So, discounting a hugely fat finger, the glass cannot overflow.

Apologies, then the answer is that it'll weigh the same.

There will always be gravitational pull.
Which will experience an equal and opposite reaction by dint of being hopefully attached to your hand.

So, if you had some sort of strain gauge on the crane, it would not change as the weight was lowered into the water? What if your 1000 t weight was the same density as water? What if your 1000 t weight was a boat?
It would "change" weight

#### JohnD

what if it was on a conveyor belt?

#### Softus

Ignoring, for now, the scenario of the bath overflowing
Wrong, how can it not overflow? the bath is full.
Well I ignored that scenario, for the purpose of discussing the effect of a buoyant object.

Me. I did. And quite explicitly.

Also, by implication, so did JohnD.

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