Question

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.1 m. How many people can the rafter hold before they start getting their feet wet, assuming the average person has a mass of 68 kg. Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60. Please show work and specify answer.

Answer 1

Volume of raft

= 12 * (?/4)(0.450)^2 * 6.1 m^3

= 11.6360 m^3

Buoyant force from water, F

= weight of water having same volume as raft

= 11.6360 x 1000 x 9.8 = 9.8 * 11636 N

=114032.8 N

Mass of raft

= volume x density

= 11.6360 x 600

= 6981.6 kg

n = number of persons

weight of raft + weight of persons < buoyant force

=> 6981.6 * 9.8 + 68n * 9.8 < 11636 * 9.8

=> 68n < 11636.0 - 6981.6

=> n < 68.44

=> n = 68 persons.