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Density and Floating Objects

hey.

this is a question from the internet, which i'd like to know the answer to.

if you've got a tank of water (density = 1g/cm^3) and you put a cube of an unknown material in the water. the cube floats so that exactly half its volume is above the surface of the water, and half of it is below the surface of the water.

what is the cube's density? is it the same as the water? this would make sense to me, but i'm having trouble explaining it... even if its right.

Reply 1

Wangers

If you wanted to work it out - place it in a full tub of water, measure how much water it displaces, and use the Archimedies principle.

Reply 2

teachercol

Since it is displacing half its volume

the weight of water it displaces is equal to the weigth of the object

so its density must be ....(and no its not the same density as the water)

Reply 3

MisterT

Wangers

If you wanted to work it out - place it in a full tub of water, measure how much water it displaces, and use the Archimedies principle.

the material is hypothetical.

what's the archimedes principle anyway?

Since it is displacing half its volume

the weight of water it displaces is equal to the weigth of the object

so its density must be ....(and no its not the same density as the water)

i don't follow you...

Reply 4

Morbo

Archimedes' Principle - The weight of water a floating object displaces is equal to the weight of the object.

It takes half of the object's volume to displace its own weight in water.
Its own mass would take up half its volume if it was made of water.
So...

Reply 5

MisterT

Worzo

i'm sorry. i really don't understand... :redface:

Reply 6

teachercol

Archimedes principle says that a floating object displaces its own weight in water.

So the weight of the water displaced by half the volume of the object is the same as the weight of the whole object

So the object must have half the density of water.

Reply 7

Mehh

Archimedes realised that when objects float they have a certain amount of volume underwater.
He noticed that if a load is placed on a boat the boat would float lower in the water. He found out that the amount the boat lowers is dependant on how heavy the object is, in that the volume of boat under the water is proportional to the weight of the boat. Also that (boat volume) x (density of water) = (mass of the boat).

Ok. In practice this has a few interesting consiquences. For example, when a narrow boat travels over an aqua duct, there is no change in the loading of the aquaduct. This is because the narrowboat, although has mass and hence weight, it also pushes aside an equal mass/weight of water. Thus the aquaduct becomes heavier by a certain amount of boat, but also at the same time carries less water; the two effects cancel out.

This effect is used to great effect in the Falkirk Wheel, another Millenium project. The Falkirk Wheel connects the Clyde Canal with the Union Canal in Scotland. Esentially it is a circular lift. However the wheel contains two open topped vessels which contain water. The two containers have exactly the same amount of water capacity in them, so they will weight the same no matter what (even when a boat is in them). This means that the electric motors only need to oppose the friction in the wheel, as opposed to work against gravity.

Reply 8

physicsgirlie

Mehh

Ok. In practice this has a few interesting consiquences. For example, when a narrow boat travels over an aqua duct, there is no change in the loading of the aquaduct. This is because the narrowboat, although has mass and hence weight, it also pushes aside an equal mass/weight of water. Thus the aquaduct becomes heavier by a certain amount of boat, but also at the same time carries less water; the two effects cancel out.
.

isn't that assuming that the water leaves the aqueduct? like over the sides or something?

Reply 9

teachercol

It gets pushed back into the canal.

Reply 10

Theorist

MisterT

if you've got a tank of water (density = 1g/cm^3) and you put a cube of an unknown material in the water. the cube floats so that exactly half its volume is above the surface of the water, and half of it is below the surface of the water.

what is the cube's density? is it the same as the water? this would make sense to me, but i'm having trouble explaining it... even if its right.

1. Archimedes' Principle states that an object floating in water will displace a given volume of water equal to its own weight.

2. As half of the object is below the surface of the water, the volume of water displaced is equal to half the total volume of the object.

3. However, the weight of the water displaced by the object, and the weight of the object itself are the same. Therefore, their masses are the same (as W = mg and g is a constant).

4. Using the density formula, M = ρV; we can see that: