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Topic Topic: Bernoulliís Principle: Buoyant force = Weight of displaced fluid Post ReplyNew Question
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System
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Joined: 26†June†2005
Posts: 918
Posted: 20†July†2005 at 11:44am | IP Logged Quote System

QUIZ QUESTION #316

Titanic
was the largest ship in the world when it was launched in 1912. The mass of the ship was 50000 tonnes. When Titanic was seaworthy, calculate the buoyant force that acted upon it, and the volume of seawater displaced by it.

(Use Archimedes' principle. Assume  1 tonne 1000 kg,  gravitational acceleration = 10 m/s  and  seawater density = 1025 kg/m)
    A.   Buoyant Force B = 5107
Seawater volume = 4878 m
    B.   Buoyant Force B = 5108
Seawater volume = 48780 m
    C.   Buoyant Force B = 5109
Seawater volume = 487805 m
    D.   Buoyant Force B = 51010
Seawater volume = 4878049 m
    E.   Buoyant Force B = 51011
Seawater volume = 48780488 m
 QUIZ QUESTION #316 created by Beka on 19 July 2005 at 2:01pm

Correct answer: B    Correct clicks: 36.48%  Wrong clicks: 63.52%
 
    A.   [28 clicks 17.61%] 
 
    B.   [58 clicks 36.48%] 
 
    C.   [22 clicks 13.84%] 
 
    D.   [32 clicks 20.13%] 
 
    E.   [19 clicks 11.95%] 
 
Please discuss this quiz question.
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Beka
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Joined: 26†June†2005
Posts: 27
Posted: 23†July†2005 at 7:27pm | IP Logged Quote Beka

From equilibrium of vertical forces, we know that the buoyant force acting on Titanic must equal to its weight, because Titanic is floating. Therefore we first have to calculate the weight of Titanic.

Mass of Titanic (in kg) = 50,000 tonnes  1000 = 5  107kg

Weight of Titanic = 5  107kg    10 m/s = 5  108N

There, we already found the first answer - the magnitude of buoyant force is 5  108N.

To find the second answer, we rely upon Bernoulli's principle which state that the magnitude of the buoyant force must equal the weight of the displaced liquid. We therefore know the weight of the displaced seawater and can equate it as such:

Weight of displaced seawater = 5  108N

(Mass of displaced seawater)  10 m/s = 5  108N

(Volume of displaced seawater)  1025 kg/m  10 m/s = 5  108N

 Volume of displaced seawater =
5  108N
1025 kg/m  10 m/s

Volume of displaced seawater = 48780 m

 

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