# The density of a cube.

college boy19
One end of a light thin string is attached to the bottom of a 3.7 g, 42 cm3 cork. The other end is attached to a 58 g cube. The arrangement is placed in water and it is found that with 82% of the cork submerged the cube is held in equilibrium. What is the density of the cube in g/cm3?

I need help figuring out this problem.

Homework Helper
Welcome to PF!

Hi college boy19! Welcome to PF! (try using the X2 tag just above the Reply box )

Show us what you've tried, and where you're stuck, and then we'll know how to help! college boy19
okay,
the density of an object is its mass divided by its volume:

D=m/v

so for the cube all i have in the equation is :
D= 58g/v

So i know that in order to get the density i need the volume of the cube.

this is where i am stuck.

Homework Helper
Hi college boy19! So i know that in order to get the density i need the volume of the cube.

That's not the only way to get the density …

you can also work it out from the forces on the cork college boy19
Well the forces acting on the cork are the buoyant force which is the the weight of the cork which is mg which is:

BF= 3.7*g
but gravity in SI units is 9.8kg/m^3 and I am using CGS units so gravity is 98g/cm^3
So the weight of the cork is

BF= 3.7(98)=362.6

the buoyant force = to the weight of the displaced fluid

Homework Helper
Well the forces acting on the cork are the buoyant force which is the the weight of the cork

No, the forces acting on the cork are the buoyant force, the weight, and the tension in the string.

college boy19
the buoyant force:
362.6
the weight:
mg=362.6
how do i figure out the tension in the string?

is it the buoyant force - the weight of the cube

Homework Helper
the buoyant force:
362.6
the weight:
mg=362.6

How can the buoyant force be equal to the weight?

How is buoyant force defined?
how do i figure out the tension in the string?

You have two equations for it …

one for the cork, and one for the mass …

that should be enough to solve the whole problem. 