# Physics Question Regarding Densities of Spheres

• rawr101

#### rawr101

My question is regarding finding volume and densities of spheres. I'm getting strange results, so I thought I'd find out where my methods are incorrect.

I am using a graduated cylinder to drop the spheres into with water inside. I measured the initial volume of the water before I dropped the sphere in. Then I measured it after. I now have the mass, the initial volume (ml) of water, and the final volume of water (along with the uncertainties, using hi-low method ).

Should I use the formula: Linear Mass Density = Mass/Liter?

Thanks for helping.

When you say that you now have the mass, do you mean they gave it to you already or you calculated it from the data? If you say you calculated it from the data, I see what your problem is right away. The sphere does not displace an equal mass of water, but an equal volume. If you dropped a metal ball in that wieghed one gram, and another ball of the same size made of a material so dense it wieghed 1 kilogram, they would both displace the same volume of water since the beaker is equally filled in both cases. It is when objects float that they displace an equal mass of water. There is a minor technical problem with the formula you are using and that is that you are not trying to find a linear mass density, just a density. A linear mass density is something you would measure on a rope or chain and say that it wieghs so many kilograms per meter. But that's just a technical point. If you divide the mass by the volume, you will get the density. The only other problem that comes to mind is to make sure your units are right. What is wrong with the data exactly?

LeonhardEuler said:
When you say that you now have the mass, do you mean they gave it to you already or you calculated it from the data? If you say you calculated it from the data, I see what your problem is right away. The sphere does not displace an equal mass of water, but an equal volume. If you dropped a metal ball in that wieghed one gram, and another ball of the same size made of a material so dense it wieghed 1 kilogram, they would both displace the same volume of water since the beaker is equally filled in both cases. It is when objects float that they displace an equal mass of water. There is a minor technical problem with the formula you are using and that is that you are not trying to find a linear mass density, just a density. A linear mass density is something you would measure on a rope or chain and say that it wieghs so many kilograms per meter. But that's just a technical point. If you divide the mass by the volume, you will get the density. The only other problem that comes to mind is to make sure your units are right. What is wrong with the data exactly?

The goal for me is to find the densities. I weighed the metal spheres first and then recorded the initial water volume. I dropped the sphere in and measured the current water level. I'm just curious whether the equation, Linear Mass Density = Mass/Liter, will give me the correct densities I am looking for. Or would this work:

Volume Water Displaced = Final Volume - Initial Volume
volume water displaced = volume

then density = mass/volume

Sorry for these very beginner questions, this is my first physics class .

Thanks again.

yes, this will give you the density, just rememner that you need to find density in grams per cm^3 or kg per m^3. You need to make sure you convert from volume of water to the metric system. 1000L = 1m^3.

Regards,