Question

What is the smallest number of whole logs (density = 735 kg/m³, radius = 0.088 m, length = 2.88 m) that can be used to build a raft that will carry 5 people, each of whom has a mass of 82.0 kg?

Answer 1

assumption: logs are of cylindrical shape. then their volume=pi*radius^2*length

solution:

to carry 5 people and not to sink, the weight of the whole raft has to be equal or lesser than the buyoant force.

now, buyoant force=volume of the water displaced*density of water*g

=volume of the raft*density of water*g

here volume of each log=pi*radius^2*length=pi*0.088^2*2.88=0.07 m^3

mass of each log=volume*density=0.07*735=51.45 kg

hence if total x number of logs to be used,

then total mass=x*51.45 kg

total volume=0.07*x

hence total weight of the raft+5 people system=(x*51.45+5*82)*9.8

=(504.21*x+4018 ) N

buyoant force=0.07*x*1000*9.8=686*x N

then equating the two values,

504.21*x+4018=686*x

==>181.79*x=4018

==>x=22.1

hence in total minimum 23 logs are required.