# Buoyant Force Calculation for Floating Block of Wood - Homework Question

• onrytxn
Although there are many equations that can be used to calculate buoyant force, in this case you can use the simple equation B = Wfl, where B is the buoyant force and Wfl is the weight of the fluid displaced by the block. In summary, the buoyant force acting on the 0.5 kg block of wood floating in water is equal to the weight of the fluid displaced by the block, which in this case is 4.9N.
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?

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

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.

## 1. What is buoyant force?

Buoyant force is the upward force exerted by a fluid on an object that is partially or completely submerged in the fluid.

## 2. How is buoyant force calculated?

Buoyant force is equal to the weight of the fluid that the object displaces. It is calculated by multiplying the density of the fluid by the volume of the displaced fluid and the acceleration due to gravity.

## 3. What is the relationship between an object's density and buoyant force?

If an object's density is greater than the density of the fluid it is submerged in, it will sink. If the object's density is less than the density of the fluid, it will float. The greater the difference in density, the greater the buoyant force.

## 4. Does the shape or size of an object affect buoyant force?

Yes, the shape and size of an object can affect the amount of buoyant force it experiences. Objects with larger surface areas will experience more buoyant force, while objects with smaller surface areas will experience less buoyant force.

## 5. Can buoyant force act in any direction?

No, buoyant force always acts in an upward direction. This is due to the fact that fluid pressure increases with depth, causing a greater upward force on the object at the bottom than on the top.

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