Natiphy2007 asked: Advertisements for a certain, small car claim that it floats in water.If the car’s mass is 880kg , and its interior volume is 3.3 m^3, what fraction of the car is immersed when it floats? You can ignore the volume of steel and other materials.
Express your answer using two significant figures.
B) Water gradually leaks in and displaces the air in the car. What fraction of the interior volume is filled with water when the car sinks?
Express your answer using two significant figures.
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Use Archimedes’ Principle :
Buoyant force = Weight of water displaced
Weight of car = Volume immersed x Density of water x g
In the second part, Buoyant force should be equal to Weight of car + Weight of water inside the car
Try solving it further.
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We ignore the volume of steel and other materials.
Volume of car = V =3.3 m^3
Mass of car = m =880 kg
weight of car = 880*g N
Let the volume of displaced water = v
weight of displaced water = v*d*g=1000v*g N
For floatation of car,
weight of displaced water = weight of car
1000vg=880g
v =880/1000 =0.88 m^3
Fraction of volume immersed = v/ V =0.88/3.3= 88 /330 =0.27
fraction 0.27 of the car is immersed when it floats
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Edited.
B ) The car will sink when weight of car plus weight of water inside weighs more than weight of water displaced by the complete car inside water
Volume of water = v
Weight of water inside car= w1 =vdg=1000vg
Weight of the car (without water) = w2 =880g
weight of water displaced by the complete car inside water= W= Vdg=3.3*1000*g=3300g
w1 + w2 = W
1000vg + 880g = 3300g
1000v=2420
v=2.42 m^3
v / V =2.42/3.3=0.7333
The fraction of the interior volume when the car sinks is 0.7333
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