A rectangular, flat-bottomed boat is at port waiting to be filled with cargo. Th

Question

A rectangular, flat-bottomed boat is at port waiting to be filled with cargo. The empty boat
with crew and equipment has a mass of 1.5 x 10^8
kg and has dimensions of 400 m (length) x 60 m (width) x 30 m (height). Remember the density of sea water is 1030 kg/m ^3.
(a) When empty how far is the bottom of the boat beneath the water line?
(b) The boat takes on 2.6 x 10^8 kg in cargo. How high above the water is the top edge of the
boat after adding the cargo?
(c) Because another boat has broken down, the captain agrees to take on additional cargo. If his
route takes him past a point that is only 22m deep, how much additional cargo can he take on
and leave 1 m between the bottom of his boat and the seafloor?

Explanation / Answer

buoyancy force = Volume of displaced water * density * g
a) let h is the part of boat beneath the water
h* 400*60*1030*9.81= 1.5*108
h= 0.618 m

b) in second case let h is the part of boat beneath the water
h* 400*60*1030*9.81= 1.5*108 + 2.6 *108
h=1.6906 m

therefore top edge of the boat above water = 30- 1.6906 =28.31 m

c) maximun h for this case can be = 21 m

for this total load can be estimated as above method
21* 400*60*1030*9.81= M

additional cargo = M - ( 1.5*108 + 2.6 *108) = 4682567200 kg

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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