quiz question

[Doctor]

There is a lake that is perfectly smooth.
You are in a rowing boat on this lake, and in the boat with you is a metal weight.
A Friend marks the water level of the lake.
You then chuck the weight overboard into the water.
When the ripples have settled, and is perfectly smooth again, the friend remarks the water level, has the water level of the lake gone up, gone down or remained the same?
And why?

 

[Max Power]

:?

 

[cambournepete]

Down.

While in the boat the weight was displacing a volume of water equal to its weight.
While in the water the weight is displacing its volume of water, which is less, so the water level falls slightly.

 

[Lord Nibbo]

It's stays the same.

 

[RogerS]

I'm with Pete.

 

[mailee]

Stays the same is my guess. :?

 

[Oryxdesign]

It goes down by the difference between the volume of the weight and the relative density of the material the weight is made of, presuming the RD is over 1.

(volume of water equal to weight of metal weight-volume of weight) / surface area of lake

assuming surface area does not change significantly

Simon

 

[Steve Maskery]

+1 for Pete.
A floating object displaces its own mass (say 2kg, which equals 2L of water), a submerged object displaces its own volume (say 1L).
So if the weight is 1L in volume but weighs 2KG, when it drops the water drops too, because there is only 1L of water being displaced now whereas there were 2L being displaced before.

Edit - I can't type fast enough.

 

[RogerS]

Can I change my mind?

This explanation from a physicist friend of mine. Mind you he got the aircraft on the treadmill wrong !

Up thrust equals down thrust equals weight of water displaced. Increase in level! Doesn't matter if the weight is in the boat or outside of it in the water. The sum is the same.

 

[Gary]

I'm with Rogers amended answer.

Archimedes principle states the up thrust should be equal to the weigh of the fluid displaced.

Hence the level should remain the same.

 

[Lord Nibbo]

Can I change my mind?

This explanation from a physicist friend of mine. Mind you he got the aircraft on the treadmill wrong !

Up thrust equals down thrust equals weight of water displaced. Increase in level! Doesn't matter if the weight is in the boat or outside of it in the water. The sum is the same.

Spot on Roger. Very simply put.

 

[Eric The Viking]

Pete's right:

When it's in the boat, the weight displaces the equivalent weight of water.
When it's at the bottom of the lake, it displaces the equivalent volume of water.

Now iron/steel is more dense than water, so the volume for a given weight is smaller. Thus, once the weight leaves the boat, the water level goes down slightly, as the weight is displacing a smaller volume than it did in the boat.

At least, it seemeth so to me.

E.

 

[barkwindjammer]

+1 for Erics hypotheses, as the weight is pushing the hulls surface area its displacing more water than when it leaves the boat and can only displace its own volume of water

 

[softtop]

I would say it depends on the density of the weight, and indeed the relative weight/size of the boat.

Let's assume you are in a large boat with a tiny but VERY heavy weight. Then the water displaced by the boat being pushed down is much more than the volume of water from the weight when you toss it in. Hence it goes down.

However, if the weight is very light but large, and you are in a very small boat then the water displaced by the boat may be virtually nothing yet the weight will again displace its volume, hence it goes up.

 

[Steve Maskery]

Nope. It only matters whether it floats or sinks, not how much it floats or sinks. The boat itself is irrelevant. If the weight sinks the water level drops too.
S

 

[barkwindjammer]

The weight of the 'weight' is irrelevent, it its volume thats important

 

[softtop]

Okay, yes since the weight must be denser than water in order to sink (and reviewing the OP it does say made of metal) it MUST displace more water by weight than it does by volume. Hence my second option cannot apply here, so it goes down.

 

[Anonymous]

where is he marking the water level whilst sitting in the boat in the middle of the lake?

 

[squib]

The boat floats higher and the lake stays the same.

 

[Lord Nibbo]

Pete's right:

When it's in the boat, the weight displaces the equivalent weight of water.
When it's at the bottom of the lake, it displaces the equivalent volume of water.

Now iron/steel is more dense than water, so the volume for a given weight is smaller. Thus, once the weight leaves the boat, the water level goes down slightly, as the weight is displacing a smaller volume than it did in the boat.

At least, it seemeth so to me.

E.

You state (When it's at the bottom of the lake, it displaces the equivalent volume of water.)

You forget the boat now displaces less too

Put it this way.....if I take a pee from a boat the water level will stay the same, it don't matter if I pee a pint of a thousand gallons