Physics help

[Tan008]

For those who are using EK, it's a 30 minute exam question for lecture #5 (#113).

 

A brick sits on a massless piece of Styrofoam floating in a large bucket of water. If the Styrofoam is removed and the brick is allowed to sink to the bottom:

 

A. the water level will remain the same

B. the water level will fall

C. the water level will rise

D. the density of the brick must be known in order to predict the rise or fall of the water level

 

the correct answer is B, but I can't seem to reason it out, and I don't understand the EK explanation. Any help would be appreciated

[The Law]

I think it's because when the brick is on the styrofoam the weight of the water it is displacing is brick + styrofoam, so when you remove the sytrofoam, then the amount of water it displaces will be less... I think... causing the water level to fall

[AMmd]

I think it's because when the brick is on the styrofoam the weight of the water it is displacing is brick + styrofoam, so when you remove the sytrofoam, then the amount of water it displaces will be less... I think... causing the water level to fall

 

yeah thats what i think too

[avenir001]

When u get a question like this, it also helps to blow things out of proportion to make it more intuitve...imagine a small brick sitting on a huge, much lighter styrofoam...the brick is heavy and will push down on the styrofoam to submerge a big enough portion of it to displace enough water to provide the upward buoyant force that's equal to the weight of the brick & styrofoam and keeps them floating. When u get rid of the styrofoam, the much smaller brick will sink because the volume of water it displaces (ie the same as its own small volume) is not enough to balance the weight of the brick. So which would displace more water and cause the water level to rise, a huge styrofoam that's mostly submerged or a small brick that's entirely submerged?

[THX]

For buyouncy, think of this way: If something floats, it is displacing its weight in volume of water. On the other hand, if something sinks, it is displacing its volume in weight of water.

 

ie. to be clear in regards to the question. If something sinks, it's weight is not proportional to the amount of water volume displaced. But if it floats, its weight is proportional to the amount of water displaced.

[Guest amar21]

I think it's because when the brick is on the styrofoam the weight of the water it is displacing is brick + styrofoam, so when you remove the sytrofoam, then the amount of water it displaces will be less... I think... causing the water level to fall

 

but it says that the styrofoam is massless... so W = mass x gravity .. and that means you shouldnt even be taking into account or reasoning that the styrofoam + brick = 'more weight' than 'brick' alone.

[THX]

Yes, the Styrofoam is massless, but because of its large surface area it reduces the density of the brick so that it is lower than the density of water. Smaller density than water = floats. But if it floats, it must displace its weight in volume of water. Therefore, weight of brick = weight of water displaced. On the other hand, remove the Styrofoam and suddenly the density of the brick is larger than water and the weight the of fluid displaced is equal to the volume of the brick. Hence, if less weight of water is displaced, less volume of water is displaced compared to a floating brick, hence the water level drops by removing the styrofoam. (a bit convoluted answer, but I hope it helps)

 

edit: oops, didn't read the quote properly

[The Law]

but it says that the styrofoam is massless... so W = mass x gravity .. and that means you shouldnt even be taking into account or reasoning that the styrofoam + brick = 'more weight' than 'brick' alone.

 

Ooh, I misread it.

Even still, I hate fluids. hahaha

[Tan008]

Yes, the Styrofoam is massless, but because of its large surface area it reduces the density of the brick so that it is lower than the density of water. Smaller density than water = floats. But if it floats, it must displace its weight in volume of water. Therefore, weight of brick = weight of water displaced. On the other hand, remove the Styrofoam and suddenly the density of the brick is larger than water and the weight the of fluid displaced is equal to the volume of the brick. Hence, if less weight of water is displaced, less volume of water is displaced compared to a floating brick, hence the water level drops by removing the styrofoam. (a bit convoluted answer, but I hope it helps)

 

edit: oops, didn't read the quote properly

 

That makes sense, thanks . That whole massless Styrofoam had me a bit confused.

[spoudaios]

what is the connection between surface area and density?

[THX]

Well, in the example given, the brick lies on a large Styrofoam board. This decreases the overall density, as there is less weight per unit of measurement.