Solving for Fluid Density: A 2.0 kg Iron Block

[chara76]

Homework Statement

A 2.0 kg iron block is suspended from a spring scale and is submerged in a fluid of unknown density. The spring scale reads 2.55 N. What is the density of the fluid?

Homework Equations

Buoyant force = mass*gravity
Buoyant force = (Density of fluid)*(volume of iron block)*(gravity)

The Attempt at a Solution

2*9.81=(density)*(volume)*9.81

I can't figure out how to get the volume to solve for the density.

 

[Cyosis]

The equality you've written down claims that the block is floating in the liquid. Don't forget the block is attached to a spring which exerts an upward force on the block as well. Secondly you know that the buoyant force is equal to the weight of the displaced volume. Since the block is fully submerged that volume must be the same as the volume of the block.

 

[chara76]

So,

Buoyant force + 2.55 N = (mass)*(gravity)
Buoyant force = 17.07 N

17.07 N = (density)*(17.07 N)*9.81

density=.101937

Is this right?

 

[Cyosis]

No you plugged the value for the buoyant force into the volume of the buoyancy equation in your last step. You will need to find the volume that is displaced by the block, which is equal to the volume of the block because it is emerged in the fluid. Hint: look up the density of iron.