Archimedes' principle explains why objects feel lighter in water and why some objects float while others sink. When an object is placed in a fluid, it pushes some of the fluid out of the way. The fluid pushes back upward with a buoyant force.
This idea is essential for understanding boats, submarines, hot air balloons, and density measurements.
The buoyant force equals the weight of the fluid displaced by the object. If the buoyant force is greater than or equal to the object's weight, the object can float or rise. If the object's weight is greater than the maximum buoyant force available, it sinks.
Apparent weight is the measured weight of an object in a fluid, reduced by the upward buoyant force.
Key Facts
- Archimedes' principle: F_b = weight of displaced fluid
- Buoyant force: F_b = rho_fluid V_displaced g
- Weight of an object: W = mg
- Apparent weight in a fluid: W_app = W - F_b
- An object floats when F_b = W and only enough volume is submerged to displace its own weight of fluid.
- An object sinks if its average density is greater than the fluid density, so rho_object > rho_fluid.
Vocabulary
- Buoyant force
- The upward force a fluid exerts on an object placed in it.
- Displaced fluid
- The volume of fluid pushed aside by an object when the object is submerged or floating.
- Apparent weight
- The weight an object seems to have when measured in a fluid, equal to its true weight minus the buoyant force.
- Density
- Mass per unit volume, calculated using rho = m / V.
- Equilibrium
- A state where forces balance, such as a floating object with upward buoyant force equal to downward weight.
Common Mistakes to Avoid
- Using the total object volume instead of the displaced volume. This is wrong for floating or partially submerged objects because only the submerged volume displaces fluid.
- Forgetting that buoyant force depends on the fluid density. The same object experiences a larger buoyant force in salt water than in fresh water if the displaced volume is the same.
- Assuming a floating object has no weight. A floating object still has weight, but the buoyant force balances it.
- Adding buoyant force to weight when finding apparent weight. Apparent weight is smaller than true weight in a fluid because the buoyant force acts upward, so W_app = W - F_b.
Practice Questions
- 1 A metal cylinder displaces 0.0020 m^3 of water when fully submerged. If water has density 1000 kg/m^3 and g = 9.8 m/s^2, what buoyant force acts on the cylinder?
- 2 A block weighs 50 N in air and has an apparent weight of 32 N when submerged in water. What is the buoyant force on the block, and what volume of water does it displace if rho_water = 1000 kg/m^3 and g = 9.8 m/s^2?
- 3 A large wooden block and a small steel ball are placed in water. Explain why the wooden block can float even though it is larger, while the steel ball sinks.