Calculating Potential Energy of Buoyant Force: Understanding Density and Depth

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In summary, the conversation revolved around calculating the potential energy due to the buoyant force in a homework problem. The participants discussed using calculus and the given variables to solve for the potential energy. They also clarified the units of 'r' and the role of density in the equation. The final equation was determined to be pgvd - mgd, with consideration for the correct density to use.
  • #1
clipperdude21
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I am pretty sure i know how to answer my homework problem if someone can tell me how to calculate the potential energy due to the bouyant force? I am assuming its Fr but what is r and where would you get it from?

In the problem i am given the depth from the surface at which an object is at.

THANKS!
 
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  • #2
Assuming a 1D problem and a calculus based class, I'd use F = - (d/dx) V

Where F is the buoyant force and V is the potential energy associated with the buoyant force. (d/dx) is a spatial derivatve. Solve this equation for V by integration.
 
  • #3
You need to give more information. There is NO potential energy due to a force alone. Potential energy is the work a force could (or would be done against the force) in moving an object. No motion- no work. You have to be given the distance in the problem. Exactly what does the problem say?
 
  • #4
Well he said he was given the depth from the surface that the object was located and it should float that distance to the surface.

If your class isn't calculus based, figuring out the units of 'r' should get you started.
 
  • #5
ok i think i got it... the problem is basically all variables and says you drop a sphere of mass m , volume v and density p into water. The sphere drops to a distance d below the surface of the water. What it the total potential energy due to gravity and the bouyant force. It then says to assume p is lower than water. I think this would be the sphere rising to the top? so the distance the bouyant force pushes up is d so the energy is pgvd + the gravitational potential energy and that's -mgd. the total would be...

pgvd - mgd right?
 
  • #6
Careful with your densities, the p given is different than p(water). Remember the buoyant force in water is equal to the weight of *water* displaced. Also, remember that only a *change* in potential energy is meaningful, what you calculated is the change in potential energy as the sphere rises to the surface.

To answer your question, is p or p(water) a better fit for your final equation?
 

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. It is a result of the difference in pressure between the top and bottom of the object.

2. How is buoyant force calculated?

Buoyant force is calculated by multiplying the volume of the displaced fluid by the density of the fluid and the acceleration due to gravity. This can be represented by the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. What factors affect buoyant force?

The buoyant force on an object is affected by the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. It is also affected by the shape and size of the object, as well as the depth at which it is submerged.

4. What is the relationship between buoyant force and an object's weight?

According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid it displaces. This means that if the buoyant force is greater than the object's weight, it will float; if the buoyant force is less than the object's weight, it will sink; and if the buoyant force is equal to the object's weight, it will remain suspended at a specific depth in the fluid.

5. How is buoyant force used in everyday life?

Buoyant force plays a role in many everyday activities, such as swimming, boating, and scuba diving. It is also used in the design of ships and submarines, as well as in the function of life jackets and flotation devices. Additionally, buoyant force is used in industries such as oil extraction and sewage treatment, where it helps to separate different substances based on their density.

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