Is bouyant force frame independent ? . I mean if we have an accelerated beaker would the bouyant force be Vp(g+a) in both frame of reference ? and

To address whether buoyant force is frame independent, we need to delve into the principles of buoyancy and how forces behave in different reference frames. Buoyant force arises from the pressure difference exerted on an object submerged in a fluid, and this pressure difference is influenced by the gravitational field acting on the fluid and the object itself.

Understanding Buoyant Force

Buoyant force can be described by Archimedes' principle, which states that the upward buoyant force experienced by a submerged object is equal to the weight of the fluid that the object displaces. Mathematically, this is expressed as:

• F_b = ρVg

Where:

• F_b is the buoyant force.
• ρ is the density of the fluid.
• V is the volume of the fluid displaced by the object.
• g is the acceleration due to gravity.

Frame of Reference and Acceleration

When considering different frames of reference, particularly in accelerated systems, the situation becomes more complex. In a non-accelerated frame, the buoyant force is straightforward, as it depends solely on the gravitational acceleration g. However, if we switch to an accelerated frame, such as a beaker being accelerated upwards with acceleration a, we need to consider how this affects the effective gravitational field.

Effective Gravitational Field in Accelerated Frames

In an accelerated frame, the effective gravitational acceleration becomes:

• g' = g + a

Thus, in this frame, the buoyant force can be recalculated as:

• F_b' = ρV(g + a)

Comparing Frames

Now, if we compare the buoyant force in both frames, we see that in the stationary frame, the buoyant force is F_b = ρVg, while in the accelerated frame, it is F_b' = ρV(g + a). This indicates that the buoyant force is indeed dependent on the frame of reference when acceleration is involved.

Conclusion on Frame Independence

In summary, buoyant force is not frame independent when considering an accelerated frame. The presence of acceleration modifies the effective gravitational field, leading to a different calculation for buoyant force. Therefore, in an accelerated beaker, the buoyant force would be Vp(g + a) in that frame, while it remains Vp(g) in a non-accelerated frame. This illustrates how forces can vary based on the observer's frame of reference, especially in non-inertial (accelerated) frames.