Buoyant Force Calculation for Floating Block of Wood - Homework Question

[onrytxn]

Homework Statement

A 0.5 kg block of wood is floating in water. What is the magnitude of the buoyant force acting on the block.

Homework Equations

B=Buoyant force: W=weight; fl=fluid; m=mass; V=volume; DEN=density;

There are a couple of equations that our professor gave us, but I am totally confused how to use them.

B=Wfl & Wfl=Wm & Vm>Vfl & DENflVfl=DENmVm

The Attempt at a Solution

I have figured weight of the mass--W=mg, which is 4.9N

Looking at the first two equations, I would lean toward the thought that 4.9N is the answer, but that seems too easy. Am I making this more complicated than it needs to be, or I am truly as confused as I feel?

 

[Dick]

Sometimes questions are easy. You are correct - after all the block is floating.

 

[m2003]

The equation for the buoyant force is B = Wfl, where Wfl is the weight of the fluid displaced by the object. In this case, the object is floating, so the buoyant force must be equal to the weight of the object. Therefore, the magnitude of the buoyant force is also 4.9N.

You can also use the equation B = DENflVfl, where DENfl is the density of the fluid and Vfl is the volume of the fluid displaced by the object. In this case, the object is floating, so the volume of the object must be equal to the volume of the fluid displaced. You can calculate the volume of the object by dividing its mass by its density. Then, you can use the density of water (1000 kg/m^3) as the density of the fluid and solve for the buoyant force.

Overall, you were on the right track and your answer of 4.9N is correct. It is important to remember that in order for an object to float, the buoyant force must be equal to the weight of the object.