Upthrust

• The physical origin of upthrust lies in the pressure difference between the top and bottom surfaces of a submerged object.

• Fluid pressure increases with depth according to the relationship $p = h \rho g$, where $h$ is depth, $\rho$ is fluid density, and $g$ is gravitational field strength.

• Because the bottom of an object is at a greater depth ($h_{bottom} > h_{top}$), the upward pressure on the base is greater than the downward pressure on the top.

• This pressure imbalance creates a resultant force acting upwards, which we define as upthrust.

Determining Floating and Sinking

• Step 1: Compare Densities: If the object's average density is less than the fluid's density, it will float. If it is greater, it will sink.

• Step 2: Analyze Forces: Identify the weight of the object acting downwards and the upthrust acting upwards.

• Step 3: Calculate Resultant: If $Upthrust = Weight$, the object is in equilibrium and floats. If $Weight > Upthrust$, the object accelerates downwards.

• Step 4: Displacement Check: For a floating object, the weight of the fluid displaced is exactly equal to the weight of the object itself.

• It is vital to distinguish between volume and weight; upthrust depends on the volume of the submerged part, but the ability to float depends on the object's total weight relative to that upthrust.

• Misconception: Students often think upthrust only acts on objects that float. In reality, upthrust acts on every object in a fluid, including those that sink.

• Surface Area Confusion: While pressure depends on area ($F = P \times A$), upthrust is fundamentally about the volume of fluid displaced, not just the shape of the bottom surface.

• Weight vs. Mass: Ensure you use weight (Newtons) rather than mass (kg) when comparing forces in a free-body diagram.