# Homework Help: What length of steel is above the surface?

1. Feb 15, 2010

### UMDstudent

[SOLVED] What length of steel is above the surface?

1. The problem statement, all variables and given/known data

A 10-cm-diameter, 80.0 -tall steel cylinder (density of steel 7900) floats in mercury. The axis of the cylinder is perpendicular to the surface.

What length of steel is above the surface?

2. Relevant equations

Free body Diagram
Density = Mass / Volume
Buoyant Force = mass*gravity (Free Body Diagram)
Volume of a cylinder = Pi * r^2 * h

3. The attempt at a solution

Given : Radius = .05m | Height = .4m | Density of Steel = 7900 kg/m^3 | Density of Mercury 13570 kg/m^3 |

Unknowns : Mass of steel pipe ? | height above the mercury? |

First thing i did was draw a Free Body Diagram where i calculated that the Buoyant Force was equal to the mass * gravity of the pipe/rod:

Fb = mg : rho*pi*r^2*h = m (both gravity's cancel ) I can transform this formula into :

Height = Mass / rho * Pi * R^2

How do we determine mass? We know that Density = Mass/ Volume. So we get :

Mass = Volume * Density = (Pi *r^2*h)*Density = pi*.05^2*.4*7900 = 24.8 kg

Now, we plug that into the above equation (Height = Mass / rho * Pi * R^2 ) :

Height = 24.8kg/13570 * pi*.05^2 = .23 centimeters. This should be the right answer but according to mastering Physics, this is incorrect. It seem logical, where did i go wrong?

-SHANE

Last edited: Feb 16, 2010
2. Feb 16, 2010

### UMDstudent

nvm, I figured this out. I needed to just convert that answer back to centimeters and then subtract that *23 centimeters from the original 80.

Thanks.

3. Feb 16, 2010

### UMDstudent

nvm, I figured this out. I needed to just convert that answer back to centimeters and then subtract that *23 centimeters from the original 80.

Thanks.