Calculating Depth of Water in Floating Cube

[rsyodoom2005]

1. A hollow cubical box is .30 m. This box is floating in a lake 1/3 of its height beneath the surface. The walls of the box have neglibe thickness. Water is poured into box. what is the depth of the water in the box at the instant the box begins to sink? pwater= 1000kg/m3

Fb= Pfluid G V
D=M/V


okay so i got the volume of the whole of the box to be .027 m(3) then the volume of the submurged by multyplying .1m * .3m * .3m = .009m
I figure i need to know the buoyent force that is pushing up on the cube before the water is added. so i did 1000kg/m(3) (9.8m/s)(.009m) so once i get that force what i would it set it equal to! help!

 

[Kurdt]

What you need to do is find the maximum weight the displaced water can support. That means you need to find the weight of the water that would be displaced by the whole box. Now you know the weight of the box by finding how much water it displaces floating at a third of its height. Thus all you need to do is add to the box the difference between the max weight for that volume the water can hold and the weight of the box. Once you find the weight of the water you can find the volume and thus how far up the box it will need to be to just sink it.

 

[rsyodoom2005]

okay so i got the amount of the water being displaced by multypling 1000 kg/m * .009m = 9kg at 1/3 of its height. so the rest 2/3 it would take 18 kg to fill the cube right..so i divided my mass of 18kg by my density of water to get my volume.. my volume i know was .3*.3 * X= i got x to =.2m...so at .2 meter of height the cube will sink...?

 

[Kurdt]

Seems good to me.

 

[rsyodoom2005]

thanks for the help!