Archimedes Principle

1
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences

• Why do things sink or float?
• Take a container of static fluid
• Let us look at a particular volume of this fluid
• What forces act on it?
• Gravitational force
• Forces due to pressure
• Forces must add to zero as it is in static
  equilibrium.
• The difference in the forces due to pressure
  equal the gravitational force

2
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences

• If we remove the fluid from the volume, the net
  force will be equal to the weight of the removed
  (displaced) fluid but in the opposite direction.
• Buoyant Force

3
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences

• When a body is fully or partially submerged in a
  fluid, a buoyant force Fb from the surrounding
  fluid acts on the body. The force is directed
  upwards and has a magnitude equal to the weight
  of the fluid that has been displaced by the body.

4
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences
If the Buoyant force is equal to the weight of
the object, it will float. If the weight is
greater, the object will sink. The apparent
weight of an object is the weight minus the
buoyant force. Wa Wo - Fb
5
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences

• A car of mass 20000kg falls into a river. A crane
  is called to lift out the car. What is the
  minimum force the crane is required to exert to
  bring the car to the surface of the water?
• Assume the volume of the car is 5.5m3 and the
  density of water is 998kg/m3.

6
Archimedes Principle
Physics 131 - Physics for Health, Life and
Environmental Sciences

• Six children of weight 1956N make a log raft by
  lashing together logs of volume 0.08m3. How many
  logs will be required to keep them afloat in
  water with density 998kg/m3.
• Assume the density of wood is 800kg/m3.