Archimedes Principle

Activity Make groups of four. Used with permission from Microsoft

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 𝐹 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = 𝐹 𝑏𝑜𝑡𝑡𝑜𝑚 + 𝐹 𝑡𝑜𝑝 𝐹 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 =∆𝑃A Remember 𝐹=𝑃𝐴, so… 𝐹 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 =∆𝑃A Remember ∆𝑃=𝜌𝑔ℎ, so… 𝐹 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 =𝜌𝑔ℎ𝐴 Since V=ℎ𝐴 and 𝜌= 𝑚 𝑉 , so… 𝐹 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 =𝑚𝑔= 𝐹 𝑔, 𝑤𝑎𝑡𝑒𝑟 Used with permission from Microsoft

Therefore, If an object floats, the weight of the displaced fluid must equal the weight of the object. 𝜌 𝑜𝑏𝑗𝑒𝑐𝑡 𝐴ℎ𝑔= 𝜌 𝑓𝑙𝑢𝑖𝑑 𝐴𝑦g (y=height of object under the fluid) Simplify the equation: 𝜌 𝑜𝑏𝑗𝑒𝑐𝑡 ℎ= 𝜌 𝑓𝑙𝑢𝑖𝑑 𝑦 Used with permission from Microsoft

Test it Out 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? 𝜌 𝑜𝑏𝑗𝑒𝑐𝑡 ℎ= 𝜌 𝑓𝑙𝑢𝑖𝑑 𝑦 550 𝑘𝑔 𝑚3 ∗0.3m= 1000 𝑘𝑔 𝑚3 ∗𝑦 𝑦=0.165𝑚=16.5𝑐𝑚 h y