Buoyancy problem

Ed Reid

I assume that two brim full buckets of water in perfect balance will remain in balance if a boat is added to one of them since the boat will sink until it displaces its own weight of water. However, I can't work out whether this would also be true if a steel ball suspended on a thread were submerged in one of the buckets. Would that bucket now be heavier, lighter or remain the same? Regards Ed

Woody

I take it that the assumption is that the water displaced by the boat just pours over the rim of the bucket and is lost.
(no dribbling down the sides etc...)

The key to steel ball is the tension in the thread it is suspended from,
If you include a spring balance in the thread, then you will note that the apparent weight of the steel ball (as measured by the spring balance)
will appear to reduce, by exactly the amount needed to match the weight of water displaced.

Ed Reid

I take it that the assumption is that the water displaced by the boat just pours over the rim of the bucket and is lost.
(no dribbling down the sides etc...)

The key to steel ball is the tension in the thread it is suspended from,
If you include a spring balance in the thread, then you will note that the apparent weight of the steel ball (as measured by the spring balance)
will appear to reduce, by exactly the amount needed to match the weight of water displaced.
Does that mean that the weight "lost" to the ball has transferred itself into the bucket and therefore the two buckets remain in balance?

Woody

Yes,
the buoyancy from the water lifting the ball will exactly match the weight of the water displaced from the bucket.
(If you cut the thread, the bucket with the ball in it will become the heavier of the two).