8/6/2015
Archimedes Principle
Activity
• Make groups of four.
Used with permission from Microsoft
1
8/6/2015
Definition
• When an object is either completely or partially
submerged in a fluid, a buoyant force is exerted
on the object by the fluid. The amount of force is
equal to the weight of the fluid displaced by the
object.
Used with permission from Microsoft
Derivation
• 𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = 𝐹𝑏𝑜𝑡𝑡𝑜𝑚 + 𝐹𝑡𝑜𝑝
▫ Remember 𝐹 = 𝑃𝐴, so…
• 𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = ∆𝑃A
▫ Remember ∆𝑃 = 𝜌𝑔ℎ, so…
• 𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = 𝜌𝑔ℎ𝐴
𝑚
▫ Since V = ℎ𝐴 and 𝜌 = 𝑉 , so…
• 𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = 𝑚𝑔 = 𝐹𝑔,𝑤𝑎𝑡𝑒𝑟
Used with permission from Microsoft
2
8/6/2015
Therefore,
• If an object floats, the weight of the displaced
fluid must equal the weight of the object.
▫ 𝜌𝑜𝑏𝑗𝑒𝑐𝑡 𝐴ℎ𝑔 = 𝜌𝑓𝑙𝑢𝑖𝑑 𝐴𝑦g
 (y=height of object under the fluid)
• Simplify the equation:
▫ 𝜌𝑜𝑏𝑗𝑒𝑐𝑡 ℎ = 𝜌𝑓𝑙𝑢𝑖𝑑 𝑦
Used with permission from Microsoft
Test it Out
h
• A student drops a 60 g wooden
cube into a pool and watches it
float. If one of the cube’s edges
is 30 cm and has density of
550 kg/m3, how far is it
submerged?
▫ 𝜌𝑜𝑏𝑗𝑒𝑐𝑡 ℎ = 𝜌𝑓𝑙𝑢𝑖𝑑 𝑦
y
▫ 550
𝑘𝑔
𝑚3
𝑘𝑔
𝑚3
∗ 0.3m = 1000
∗𝑦
▫ 𝑦 = 0.165𝑚 = 16.5𝑐𝑚
3