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Eamonn

Passing the test or lighting the fire ?

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There are a couple of answers.

 

First, it falls into the "If you were a tree what type of tree would you be? category of getting the questionee to pontificate and allows the questioner some insight into the mind of the questionee. Somewhat difficult to do with an Internet forum.

 

Second, manhole covers, usually made of iron and big enough so a man may fit through the opening it covers are very heavy. Round makes them easy to roll when on edge. Also, being round, they won't accidentally slip through the hole they are made to cover if oriented in the wrong way - thus preventing what could be a very problematic accident.

 

How'd I do? :-)

 

 

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Acco, you are correct in your second statement.

Round is the only shape that would prevent them from falling into the hole if misaligned.

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The rate of sinking has nothing to do with it. FScouter got the answer but I don't quite follow his last statement about rate.

 

You asked for replies without an explanation that would give away the answer. It depends on the density of the brick, and a solid gold brick should sink faster than a plastic brick or a hollow brick.

 

The density of the brick affects the amount of water displaced. A heavy object in the boat will cause the boat to displace more water. When the heavy object is tossed overboard, the boat rises in the lake and the lake level drops. The drop is partially offset by the volume of the brick that causes the water level to rise when tossed over.

 

A very dense brick, imagine a solid gold brick, carried in the boat will cause a lot of water displacement because the boat drops deep into the water. (Im guessing that the weight of the object carried in the boat would be equal to the weight of the water displaced by the boat.) A much less dense brick, imagine a plastic brick or a hollow brick, will not cause the boat to ride low in the water and wont result in nearly as much rise in the lake level. Either brick however, when tossed overboard will displace exactly the same amount of water.

 

If the brick was a plastic bag filled with water, (ignoring the weight of the bag), was tossed overboard, there should be no rise or fall at all. The boat would rise in the water lowering the lake level, and the lake level would rise by the same amount from the volume of the water brick tossed overboard. Similarly, if a bucket of water carried on the boat was poured into the lake, the level would remain the same, because the density of the water in the bucket is the same as the water in the lake.

 

If the brick floats, someone else will have to explain but Id guess there would be no change in level.

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Excuse my slide back to the basketry discussion for a minute. . . I just had a "things that make you go Hmmmm?" moment.

 

Just came back from summer camp (had to leave a day early) and there were numerous basketry merit badge blue cards completed, but . . .

 

I don't recall seeing a single basket anywhere in our site; neither being worked on nor a completed one. I must have missed something. For that matter, I haven't seen a camp stool seat for several years.

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In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. An object which sinks completely displaces an amount equal to its volume; Archimedes' Principle states that when this happens, the weight of the object is reduced by its volume times the density of the fluid. If it is less it floats.

 

Once a person knows the principle, then answers to many questions about the subject can be answered. FB

 

 

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I always vexed my teachers when they proposed questions like Acco's - I'm often accused of taking things too literally sometimes, rather than hypothetically. For the physics question proposed, I would have looked at all the elements of the question and formulated the following answer:

 

There is no change in the relative lake level. Displacement theories aside, the fact is that you, your boat, and that brick aren't of size enough to affect the displacement level of a lake in the first place. The amount of water displaced by your 200 pounds or so of boat, brick and body is insignificant on a lake - like the amount of air displaced by a flying mosquito. Because you don't affect the lake level from the start, no matter what you do with the brick - drop it overboard, throw it in the air, toss it on to shore - you won't make any difference in the relative level of the lake.

 

CalicoPenn

 

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CalicoPenn,

 

It's no wonder your instructor would be vexed. Sure there wouldn't be a measurable difference in the lake, but there would be a theoretical difference as explained by others, and given specific information such as the volume of the lake, mass of the brick, etc. the diffence could actually be calculated, (anyone recall exponents?)

 

I wasn't going to post this, but this thread has wondered sufficiently where I will. Acco's questions reminded me of a delightful little ditty by Tom Paxton.

 

SA

 

I Don't Want a Bunny Wunny

Words and Music by Tom Paxton

 

President Carter got into his boat;

Wasn't in a hurry, wanted to float.

Think about the country, think about sin.

Along swum a rabbit, and he tried to climb in.

(spoken) "And what did Jimmy say?"

 

[Cho:]

"I don't want a bunny wunny in my little row boat,

In my little row boat in the pond.

For the bunny might be crazy and he'll bite me in the throat,

In my little row boat in the pond."

 

Look at him swimming, look at him fly,

Ears laid back and a gleam in his eye!

Hissing through his front teeth, swimming like a seal!

If you were the President, how would you feel?

You'd prob'ly say,

 

[Cho:]

 

President Carter saved the day;

Splashed with the paddle, rabbit swam away.

Jimmy was a hero, felt it in his bones,

Said in the words of John Paul Jones,

 

[Cho:]

 

 

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SA,

 

Where were you when I was in school? You gave me an idea that would have been even more fun! Ask the instructor to calculate the change of lake level assuming a 5 pound brick and a 90-acre lake with an average depth of 14 feet. It would be interesting to see if s/he had a calculator that would have enough digits after the zero to come up with the answer.

 

Now that would have been wicked fun!

 

Calico

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Calico,

A smart teacher would simply reply that the question could not be answered since the relative density of the brick was not given.

 

The brick while in the boat displaces the same amount of water as it weighs (mass). Once the brick is placed in the water and sinks to the bottom, the displacement of the water is the volume of the brick. But mass is still transfered to the bottom surface. I.E, an anchor digs deeper in to the mud than a sponge. That mass was displacing water whilst in the boat, but now is transfered to the bottom surface. The difference between the mass of the volume of water displaced and the mass of the brick is the delta in the surface level of the lake. The only way to calculate that difference is to know its relative density of the brick vs. water.

 

 

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Actually as I recall the easier problems were the ones that had an actual number to calculate, even if the result ended up being some number X 10E-23. The hard problems were the ones that either had answers like 0, 1 or infinity.

 

I can recall one problem on a Physical Chemistry final that required calculating the finite probability of all the air spontaneosly rushing out of the lecture hall. It's been close to 30 years so I forget the specifics.

 

SA

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