Solving for Density: Buoyant Force & Force of Gravity

[Avalanche]

Homework Statement

Homework Equations

density = mass/volume
F_B = rho_o v_og for a floating object
F = mg

The Attempt at a Solution

Buoyant force = force of gravity due to the board
rho_o v_o = m

v_o = area*height submerged
v_o = 2.4*.05
v_o = 0.12 m^3

volume of the board = thickness*area
= 0.15*2.4
= 0.36 m^3

To find the density of the board, I need to know the mass of the board. I tried using the buoyant force of a floating object, but I need the density of the object.

Any help?

 

[voko]

For a body to be afloat, the mass of water displaced by its submerged part must be equal to the mass of the entire body. Which you have derived in the form rho_o v_o = m. What else do you need to compute the density?

 

[Avalanche]

I need the mass of the object. How do I find that?

Is rho_o equal to the density of water?

 

[2h2o]

I think I may understand where you are confused. You can calculate how much mass is displaced, but you need to consider the full geometry of the board to find its average density.

 

[voko]

Is rho_o equal to the density of water?

What else could that be? See #2 above.

 

[2h2o]

I need the mass of the object. How do I find that?

Is rho_o equal to the density of water?

You should always start with intuition. Would the plank be floating if its density were equal to that of water?

Does styrofoam float on water? Is it more or less dense than water?

 

[Avalanche]

For a body to be afloat, the mass of water displaced by its submerged part must be equal to the mass of the entire body. Which you have derived in the form rho_o v_o = m. What else do you need to compute the density?

So the mass of the board= density of water*volume of water displaced
Because the object is floating, the volume of the water displaced is equal to the volume of the submerged part.
so volume of water displaced = v_o = 0.12 m^3

= 1000*0.12
=120 kg

density of boat = m/v

=120/0.36
= 333.3 kg/m^3

Is my thinking correct?

 

[2h2o]

Is my thinking correct?

Does the solution seem reasonable? How could you check?

Here's a hint. :-)