Finding Density of a Floating Block

[superjen]

A uniform block of height 0.260 m, floats in water of density 1000 kg/m3. The bottom of the block is 0.2530 m below the surface of the water. What is the density of the block?

fb = mg
m=(pf)(v)
d = m/v

What i did was find the mass, using the volume of what is submerged, then when i found d using equation 3, i used the v of the whole block.
I know I am mixing something up here, but I am not sure what it is..

 

[mgb_phys]

The total weight of the block must equal the weight of water displaced.
If the block was the same density as water all of it would be under the surface, if it was half the density of water half of it would be below the surface.
What proportion is below the surface?

 

[nlightner]

Hello,

It seems like you are on the right track with your calculations. To find the density of the block, you will need to use the formula d = m/v, where d is density, m is mass, and v is volume.

To find the mass of the block, you correctly used the equation m = (pf)(v), where p is the density of water and f is the fraction of the block that is submerged. In this case, the block is fully submerged, so f = 1. You also correctly used the volume of the submerged portion of the block.

However, to find the density of the block, you will need to use the total volume of the block, not just the submerged portion. This is because density is a measure of mass per unit volume, and we want to find the density of the entire block, not just the part that is submerged.

So, to find the density of the block, you can use the equation d = m/v, where m is the mass you calculated using the volume of the submerged portion, and v is the total volume of the block. This will give you the density of the block in units of kg/m^3, which is the same unit as the water density given in the problem.

I hope this helps clarify the confusion. Keep up the good work!