A raft has a surface area of 100m^2 and a height of 10.0cm. If it is constructed

Question

A raft has a surface area of 100m^2 and a height of 10.0cm. If it is constructed of yellow pine and floating in a lake, calculate how much of the raft will be above the waterline. Also calculate how many people with an average mass of 70.0kg can be placed on the raft to completely submerge it without sinking it.

Explanation / Answer

A raft has a surface area of 100m^2 and a height of 10.0cm. If it is constructed of yellow pine and floating in a lake, calculate how much of the raft will be above the waterline. Also calculate how many people with an average mass of 70.0kg can be placed on the raft to completely submerge it without sinking it. let (h) meter be the height [ABOVE] the waterline >> (0.10 - h) height is below the waterline >>> volume submerged (V) = A * (0.10 - h) where A = area of crossection = 100 m^2 V = 100 (0.10 - h) -------------------------------- Archi. principle >> weight of submerged object = weight of water displaced mass * g = V *density (water) *g mass = 100 (0.10 - h) *d (water) density (wood)*(total wood volume ) =100(0.10 - h) *d (water) d(wood) * (100*0.10) = 100(0.10 - h) *d (water) d(wood) = 10(0.10 - h) *d (water) ===================== d(water) =1000 kg/m^3 ---------------------- d(wood) = 10000(0.10 - h) = 1000 - 10000 h 10000 h = 1000 - d(wood) h = [1000 - d(wood)] /10000 h = [0.10 - {d(wood)/10000}] meter I do not know the density of wood >>>> put & calculate convert to centimeter>> =============================== 2) let (n) persons of mass (m=70 kg) are placed on raft so that full (0.10 m) height of wood goes inside the waterline total weight = water displaced (full volume in) n*mg + d(wood)*(100*0.10) g = [100*0.10] d(water) *g n*70 + d(wood)*(10) = [10] d(water) calculate (n) > if n = 8.56 (fraction) then only n=8 will be the answer >> because people can't be in fraction, and n =9 will make the raft SINK.

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