Solve problems involving Archimedes principles and buoyancy

Archimedes' Principle

2.5

Archimedes' Principle

	Archimedes' principle
	An object when partially or completely submerged in a fluid is acted on by a buoyant force equal to the weight of fluid displaced.

	Buoyant force, \(F\)
	\(F=\rho v g\), where F = buoyant force, \(\rho \) = density of the liquid, v = volume of liquid displaced, g = gravitational acceleration

Archimedes' principle application

Submarine
- Dives (move downwards)
  - Ballast tank is filled with water
  - Weight greater than buoyant force (W > F)
  - Submarine dives downwards
- Rises (move upwards)
  - Water is removed from tank
  - Weight less than buoyant force (W
  - Submarine moves upwards
- Constant depth @ floats
  - W=F
Hot air balloon
- Downwards
  - Temperature decrease, volume of balloon decrease
  - Volume of air displaced decrease
  - Buoyant force decreases
  - W>F
- Upwards
  - Temperature increase, volume increase
  - Volume of air displaced increase
  - Buoyant force increases
  - W
- Constant depth
  - W=F
Plimsoll line
- In cooler or denser water, ship floats more.
- In warmer or less dense water, ship sinks more.
- Goal: to ensure the ship is loaded within safety limit
Hydrometer
- In low-density liquid
  - hydrometer sinks deeper
  - give low readings
- In high-density liquid
  - hydrometer floats higher
  - give high readings

2.5

Archimedes' Principle

	Archimedes' principle
	An object when partially or completely submerged in a fluid is acted on by a buoyant force equal to the weight of fluid displaced.

	Buoyant force, \(F\)
	\(F=\rho v g\), where F = buoyant force, \(\rho \) = density of the liquid, v = volume of liquid displaced, g = gravitational acceleration

Archimedes' principle application

Submarine
- Dives (move downwards)
  - Ballast tank is filled with water
  - Weight greater than buoyant force (W > F)
  - Submarine dives downwards
- Rises (move upwards)
  - Water is removed from tank
  - Weight less than buoyant force (W
  - Submarine moves upwards
- Constant depth @ floats
  - W=F
Hot air balloon
- Downwards
  - Temperature decrease, volume of balloon decrease
  - Volume of air displaced decrease
  - Buoyant force decreases
  - W>F
- Upwards
  - Temperature increase, volume increase
  - Volume of air displaced increase
  - Buoyant force increases
  - W
- Constant depth
  - W=F
Plimsoll line
- In cooler or denser water, ship floats more.
- In warmer or less dense water, ship sinks more.
- Goal: to ensure the ship is loaded within safety limit
Hydrometer
- In low-density liquid
  - hydrometer sinks deeper
  - give low readings
- In high-density liquid
  - hydrometer floats higher
  - give high readings