Question

(a) Is the buoyant force a conservative force? (b) Is a potential energy associated with the buoyant force? (c) Explain your answers to parts (a) and (b).

Short answer

(a)The answer is yes.

(b)The answer is yes.

(c)The buoyant force is a conservative force. It does positive work on an object moving upward in a fluid and an equal amount of negative work on the object moving down between the same two elevations.

Step-by-step solution

Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

$B={\rho }_{Fluid}g{V}_{disp}$

Where$V_{disp}$ the volume of fluid is displaced and ${\rho }_{Fluid}$is the density of the fluid.

(a)Find the buoyant force is a conservative force

Yes

(b)Find a potential energy is associated with the buoyant force

Yes

Explain the answers to parts (a) and (b)

The buoyant force is a conservative force. It does positive work on an object moving upward in a fluid and an equal amount of negative work on the object moving down between the same two elevations. [Note that mechanical energy, $K+U$, is not conserved here because of viscous drag from the water.] Potential energy is not associated with the object on which the buoyant force acts, but with the system of objects interacting by the buoyant force. This system is the immersed object and the fluid.