Floating depends on upthrust and weight
Definition
Upthrust
The resultant upward force that a fluid exerts on an object within it.
- An object initially accelerates upward when upthrust is greater than weight and downward when weight is greater than upthrust.
- A floating object at rest is in equilibrium, so upthrust equals its weight and the resultant force is zero.
- As a floating object sinks farther into a liquid, it displaces more liquid and upthrust increases until it balances weight.
Density predicts floating and sinking
Definition
Density
Density is the mass per unit volume of a substance.
- An object with a lower average density than the fluid can float because it can displace its own weight of fluid before becoming fully submerged.
- An object with a greater average density than the fluid sinks because even when fully submerged, the maximum upthrust is less than its weight.
- If the object and fluid have equal densities, a fully immersed object can remain suspended when upthrust equals weight.
- A hollow steel ship floats because its large air-filled volume makes its overall average density less than that of water.
Example
Fraction submerged
- For a floating object, ρfluidVsubmergedg=ρobjectVobjectg\rho_{\text{fluid}}V_{\text{submerged}}g=\rho_{\text{object}}V_{\text{object}}gρfluidVsubmergedg=ρobjectVobjectg.
- Therefore VsubmergedVobject=ρobjectρfluid\dfrac{V_{\text{submerged}}}{V_{\text{object}}}=\dfrac{\rho_{\text{object}}}{\rho_{\text{fluid}}}VobjectVsubmerged=ρfluidρobject.
- An object of average density 750 kg m−3750\,\text{kg m}^{-3}750kg m−3 floating in water of density 1000 kg m−31000\,\text{kg m}^{-3}1000kg m−3 has 75%75\%75% of its volume submerged.
Practical
Comparing upthrust
- Apparatus: force meter, clamp stand, object, measuring cylinder, water, salt solution, cooking oil, balance, spill tray and paper towels.
- Set-up: zero the force meter and suspend the object so it hangs freely without touching the container.
- Method:
- record the object's weight WWW in air using a balance
- lower the object until it is fully immersed without touching the sides or bottom, then record the apparent weight WappW_{\text{app}}Wapp.
- calculate upthrust from U=W−WappU=W-W_{\text{app}}U=W−Wapp.
- repeat at the same immersed volume in each liquid and measure each liquid's density using ρ=m/V\rho=m/Vρ=m/V if it is not supplied.
- repeat readings, identify anomalies and calculate a mean upthrust for each liquid.
- Controls: keep the same object, immersed volume, force meter and gravitational field strength.
- Expected result: the denser liquid produces greater upthrust because the same displaced volume has greater mass and weight.
- Safety: use small stable containers, wipe spills immediately and keep the electrical balance dry.
Common Mistake
Do not claim that every object less dense than water floats in every liquid; compare the object's average density with the density of the particular fluid.
Self review
- What force condition is required for an object to float at rest?
- Why does an object denser than the fluid sink?
- Why can a hollow steel ship float?
- How is upthrust measured using apparent weight?
- How does increasing fluid density affect upthrust for the same displaced volume?
