A raft is made up of 10 logs attached together. Each is 38 cm in diameter and has a length of 6.1 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 70 kg? Do not neglect the weight of the logs. Assume the density of wood is 600 kg/m3. (15 pts)

Explanation:

volume of each raft = cross sectional area x length

= π r² x L , r is radius of raft and L is length

= 3.14 x .19 x .19 x 6.1

= .69 m³

total volume of 10 raft = 6.9 m³

mass of raft = 6.9 x 600

= 4140 kg

Let no of person which can be balanced be n

weight of n person = 70 n

total weight = 70 n + 4140 kg

buoyant force when whole of raft is submerged in water

= volume of displaced water x density of water x g

= total volume of raft x density of water x g

= 6.9 x 1000 x g

for equilibrium

buoyant force = total weight of raft and persons

6.9 x 1000 x g  = (70 n + 4140 ) x g

6900 = 4140 + 70n

70n = 2760

n = 40  approx

the entire statement is true and correct.  

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