A large rectangular raft (density 650 kg/m^3) is floating on a lake. The surface

Question

A large rectangular raft (density 650 kg/m^3) is floating on a lake. The surface area of the top of the raft is 8.2 m^2 and its volume is 1.80 m^3. The density of the lake water is 1000 kg/m^3. (a) Calculate the height h of the portion of the raft that is above the surrounding water. (b) Calculate lire magnitude of the buoyant force on the raft and state its direction. (c) If the average mass of a person is 75 kg. calculate the maximum number of people that can be on the raft without the top of die raft sinking below the surface of the water. (Assume that the people are evenly distributed on the raft.)

Explanation / Answer

Given

Density of raft r = 650 kg/m3

Density of water w = 1000 kg/m3

Volume of the raft V = 1.8 m3

Surface area of the raft A = 8.2 m2

Solution

A)

Actual height of the raft

h = V/A

h = 1.8 / 8.2

h = 0.22 m

to find the submerged height

rVg = wVsg

rV = wAhs

hs = rV/wA

hs = 650 * 0.22 / 1000

hs = 0.65h = 0.143 m

Height of the raft floating hf = h – hs = 0.35h = 0.077m

B)

Buoyant force F = wVsg

F = wAhsg

F = 1000 x 8.2 x (0.143) x 9.8

F = 11491.48 N upward

C)

when a person steps on the raft If the remaining height of the raft (hf) will start to submerge. The buoyant force for the remaining height

F’ = wVfg

F’ = wAhfg

F’ = 1000 x 8.2 x 0.077 x 9.8

F’ = 6187.72 N

weight of one person w = 75 x 9.8 = 735 N

number of persons who can step on the raft n = F’/ w

n = 6187.72/735 = 8.42

so 8 whole persons can be on the top of the ramp without sinking it

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.