Math Student Help

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.

_______________________________–

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
_____________________________
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

_________________________

This entry was posted on Thursday, September 24th, 2009 at 8:12 pm and is filed under fraction. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.