### Brain Teasers

# Cannonball

A person in a boat drops a cannonball overboard; does the water level change?

### Hint

The cannonball in the boat displaces an amount of water equal to the mass of the cannonball.### Answer

The cannonball in the boat displaces an amount of water equal to the MASS of the cannonball. The cannonball in the water displaces an amount of water equal to the VOLUME of the cannonball. Water is unable to support the level of salinity it would take to make it as dense as a cannonball, so the first amount is definitely more than the second amount, and the water level drops.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

u just said a person in a boat...u didnt say where therefore there may be no saltinity in the the water...u should speak details.

In all fairness it really doesn't matter if their it is saltwater or not. The answer and explanation is still correct. Salt water or not amount of water displaced would still be less once you drop the cannonball overboard.

I like this one, on the outset it appeared to be a typical and mundane problem but it was a serious proposition requiring a serious approach. Salinity or not, the result is the same. Randy Eatmon

The question is a good one, but I could also say that the water level stays the same. They level of the water with respect to the container that it is in does not change

The solution is wrong, but the answer is right.

If you take the cannon ball out of the boat, the upthrust on the boat will be equal to the weight of the cannon ball.

The water level will drop slightly because the boat is not displacing as much water now as it is being pushed up further. (Less of its bottom is submerged)

The mass of this volume of water is equal to the mass of the cannon ball. But as the cannon ball is more dense (which is a fair presumption in this problem although not stated, density of cannon ball > density of water) than the water, the volume of this water is greater than the volume of the cannon ball.

When the cannon ball is dropped into the water, the water rises. It rises by the volume of the cannon ball, which ... is smaller than the water change after the ball is taken out of the boat.

Density = Mass/Volume

Higher the density, the smaller the volume

If you take the cannon ball out of the boat, the upthrust on the boat will be equal to the weight of the cannon ball.

The water level will drop slightly because the boat is not displacing as much water now as it is being pushed up further. (Less of its bottom is submerged)

The mass of this volume of water is equal to the mass of the cannon ball. But as the cannon ball is more dense (which is a fair presumption in this problem although not stated, density of cannon ball > density of water) than the water, the volume of this water is greater than the volume of the cannon ball.

When the cannon ball is dropped into the water, the water rises. It rises by the volume of the cannon ball, which ... is smaller than the water change after the ball is taken out of the boat.

Density = Mass/Volume

Higher the density, the smaller the volume

I think the problem is easier to understand if the boat is in say a lock on the Panama canal where the volume of water is fixed to a relatively small amount.

Actually, by the time you had thrown the cannonball over, enough water would have evaporated so that that water level would have no choice but to get lower unless it is raining or there is a river or creek flowing into the water then equallizing the difference...

THE CHANGE ISN'T NOTICEABLE

THE CHANGE ISN'T NOTICEABLE

So but it CHANGED.

Easy teaser

Easy teaser

OK, if you say so! I'm no good at math so you could tell me anything! Good teaser, I think?

I have heard this one before, but stated in a way that is a little more clear:

A barge filled with engines (or cannonballs, doesn't matter) is floating in a lock in a canal. The level of water in the lock is marked. Then an engine is dropped overboard. What happens to the level of water in the lock? (answer: it goes down)

Great teaser, that really tests if people understand that when something is floating, it is displacing its weight in water, but if it is submerged, it only displaces it volume.

A barge filled with engines (or cannonballs, doesn't matter) is floating in a lock in a canal. The level of water in the lock is marked. Then an engine is dropped overboard. What happens to the level of water in the lock? (answer: it goes down)

Great teaser, that really tests if people understand that when something is floating, it is displacing its weight in water, but if it is submerged, it only displaces it volume.

great teaser, thanks

Feb 02, 2006

Huh? Would you mind speaking english please?

Could someone please explain for me? I feel dumb

too many long words

I'm too stupid to get it...

im not a brain scientist, or a rocket surgeon, JK, good one

Explanation:

Lets turn this into an experiment that can be done at home.

Fill a big bowl 2/3 up with water, float a smaller bowl inside, place rocks in the smaller bowl (but not enough to sink it).

Mark the water level on the big bowl with tape, then take the rocks out of the small bowl and drop them in the water.

Does the previously marked water level rise or fall?

Okay, so here is how it works.

An object under water displaces its volume of water. That is, if you drop a 1 cubic centimeter rock in water, it will displace 1 cubic centimeter of water.

An object floating in water (or in a boat floating in water) displaces its mass of water. That is, if you place a 1 gram rock in a boat, it will displace 1 gram of water.

Now we can ask the following question - given a normal rock (more dense than water, lets say its a 1 cubic centimeter rock with a mass of 3 grams)

What has more volume, the rock, or 3 grams of water? We know water has a density of 1g/cm^3, so if the rock is placed in a boat it will displace 3 cm^3 of water, but if it sinks it will only displace 1 cm^3 of water.

So, originally we were displacing 3 cm^3 by floating the rock, then by dropping the rock in the water we displace only 1 cm^3. The more water you displace, the higher the water level rises.

Lets turn this into an experiment that can be done at home.

Fill a big bowl 2/3 up with water, float a smaller bowl inside, place rocks in the smaller bowl (but not enough to sink it).

Mark the water level on the big bowl with tape, then take the rocks out of the small bowl and drop them in the water.

Does the previously marked water level rise or fall?

Okay, so here is how it works.

An object under water displaces its volume of water. That is, if you drop a 1 cubic centimeter rock in water, it will displace 1 cubic centimeter of water.

An object floating in water (or in a boat floating in water) displaces its mass of water. That is, if you place a 1 gram rock in a boat, it will displace 1 gram of water.

Now we can ask the following question - given a normal rock (more dense than water, lets say its a 1 cubic centimeter rock with a mass of 3 grams)

What has more volume, the rock, or 3 grams of water? We know water has a density of 1g/cm^3, so if the rock is placed in a boat it will displace 3 cm^3 of water, but if it sinks it will only displace 1 cm^3 of water.

So, originally we were displacing 3 cm^3 by floating the rock, then by dropping the rock in the water we displace only 1 cm^3. The more water you displace, the higher the water level rises.

May 06, 2006

What did you say?

i agree that the water level did not change because the cannonball was in the boat which had already changed the level of the water. that was my thinking anyway.

Sorry- I'm only a B student, I didn't get it.

OK dude im pretty much something with science but.... there is an error. when the ball is taken off the boat, the mass of the ball pulls down as the force of gravity does on the person's hands. the opposite force acting on the ball is from the person, therefore, there is an upthrust as the ball is taken off. but still the answer is right.

I love teasers that make people think and compel them to share interesting comments. This teaser did both. My answer was a simple yes, I didn't feel the need to equate but I can see why most did as it is in the science category. Good one!

What grade of science does this one need?

I like that, very clever - and more knowledge to add to my increasing arsenal of useless trivia

eh,

u mean RISE, not fall

nice teaser, bad answer

u mean RISE, not fall

nice teaser, bad answer

Did I miss something? That is probably the most random thing I've ever heard. I did not understamd one word in the answer, and so I don't even know what it is. I am completely lost

*things

no the water rises, when u take a bath the water goes up right?

you said cannonball and i thought of pirates of the Caribbean. sorry. nice teaser

try it and ul see...

This requires some basic knowledge of buoyancy. Magic school bus basic not introductory physics class in high school basic.

Ignore anyone that said anything about upthrust (whatever that is) this is only looking at initial and final positions.

lets take a 3 kilo ball (tiny) with a density of 3000kg/m^3 (3 g/cc) (water is 1000kg/m^3 or 1g/cc).

a system (a boat with the cannon ball or the boat by itself or the cannon ball by itself) that isn't tethered will always displace an amount of water equal to its mass or its volume. Always.

since the boat with c.b. floats, it is less dense than water so it doesn't displace water equal to it's volume (some of it is clearly above the water). That means it displaces its mass. The boat has a mass of C (a constant because we don't care about the boat) + 3 kg. So it displaces an extra 3 liters of water. (3kg water = 3 L water).

After the c.b. is dropped, it sinks because it is denser than water. Since it is completely submerged, it's volume is displaced. (it has a volume of 1 L (3kg / 3kg/L = 1L)). The boat no longer displaces those 3 "extra" liters so you have 2L of water no longer displaced so the water level goes down.

Ignore anyone that said anything about upthrust (whatever that is) this is only looking at initial and final positions.

lets take a 3 kilo ball (tiny) with a density of 3000kg/m^3 (3 g/cc) (water is 1000kg/m^3 or 1g/cc).

a system (a boat with the cannon ball or the boat by itself or the cannon ball by itself) that isn't tethered will always displace an amount of water equal to its mass or its volume. Always.

since the boat with c.b. floats, it is less dense than water so it doesn't displace water equal to it's volume (some of it is clearly above the water). That means it displaces its mass. The boat has a mass of C (a constant because we don't care about the boat) + 3 kg. So it displaces an extra 3 liters of water. (3kg water = 3 L water).

After the c.b. is dropped, it sinks because it is denser than water. Since it is completely submerged, it's volume is displaced. (it has a volume of 1 L (3kg / 3kg/L = 1L)). The boat no longer displaces those 3 "extra" liters so you have 2L of water no longer displaced so the water level goes down.

All I have to say...and it's been said before...is huh?

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