13) You build a raft out of Oregon Pine logs each of length L-1.8 m strapped tog

Question

13) You build a raft out of Oregon Pine logs each of length L-1.8 m strapped together Oregon Pine has a density of Prine-530 kg/m3. The diameter of each log is d = .26 m. a) (8 points) You want your raft to be buoyant enough to carry four students, but you do not want to waste any wood. The average mass of a student is mstudent-72kg. What is the minimum number of logs needed to build a raft so that it can barely support the students? (i.e. to barely support the students the logs will be just barely completely submerged)

Explanation / Answer

13. given L = 1.8 m

rhop = 530 kg/m^3

d = 0.26 m

a. mstudent = 72 kg

so let the number of logs be n

for fully submerged log

extra load per log = (rhow - rhop)*pi*d^2*L/4

dF = (1000 - 530)*pi*0.26^2*1.8/4

dF = 44.916 N

hence

n*dF = 72*9.81*4

n = 62.9 logs

b. as this number of logs is way too much, this raft is not going to be easy to operate though

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