# Archimedes problem? density's of objects in liquids

• blaphysics
The relative density of the solid is 0.01299 kg/cm^3 and the relative density of the oil is 0.0125 kg/cm^3. Therefore, the relative density of the oil is slightly less than the relative density of the solid. In summary, the solid weighs 260N in air, 240N in water, and 250N in oil. Its relative density is 0.01299 kg/cm^3. The oil's relative density is 0.0125 kg/cm^3.
blaphysics
A solid weights 260N in air, 240N in water of a fluid density 1000kg/m^3, and 250N in oil

Determine the relative density of the solid and of the oil

I think I have already worked out the density of the solid:

Weight of water displaced = 260N - 240N = 20N

20N / 9.8 = 2.0408kg

Water density = 1kg per litre, so there is 2.0408 litres or 2040.8 cm^3

Mass of solid = 260N / 9.81 = 26.5kg

Mass/ Vol = Density = 26.5 / 2040.8 = 0.01299 kg/cm^3

If this is correct so far, how would I go about working the density of the oil, and are these figures measures of "relative density", which I understand to just be a comparison to the density of water?

Thank you!

You're doing fine, but I would suggest that you try to do things symbolically instead of calculating every step. (You'll find it much easier to get your answer.)

How would you express the weight of the solid (or the fluids) in terms of density and volume?

What you have seems reasonable to me.
To work the oil, you do the same thing you did above, only now you know volume and mass of the solid.

## 1. What is the Archimedes problem?

The Archimedes problem refers to the calculation of the density of an object in a liquid. It is named after the ancient Greek mathematician and inventor, Archimedes, who first discovered the principle of buoyancy.

## 2. How do you calculate the density of an object in a liquid?

To calculate the density of an object in a liquid, you need to know the mass and volume of the object. The density is then calculated by dividing the mass of the object by its volume. This can be expressed as D = m/V, where D is density, m is mass, and V is volume.

## 3. What is the principle of buoyancy?

The principle of buoyancy states that the upward force exerted by a fluid on an object placed in it is equal to the weight of the fluid that the object displaces. This is why objects that are less dense than a liquid will float, while objects that are more dense will sink.

## 4. How does an object's density affect its buoyancy in a liquid?

An object's density plays a crucial role in determining its buoyancy in a liquid. Objects with a lower density than the liquid will experience an upward force that is greater than their weight, causing them to float. Objects with a higher density than the liquid will experience a downward force that is greater than their weight, causing them to sink.

## 5. Can the density of an object in a liquid change?

Yes, the density of an object in a liquid can change. This can happen if the object is made of a material that can dissolve in the liquid, or if the temperature of the liquid changes. The density of a liquid itself can also change, affecting the buoyancy of objects in it.

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