While driving his 600-kg ultra-compact electric car, a distracted driver starts crossing a drawbridge. Not realizing that the drawbridge is about to open, he ends up in the river below with his car. Fortunately the car stayed afloat for a while and he is able to escape before it starts sinking. (a) If the volume of the interior is 2.0 m3, what fraction of the car is immersed while it floats? (b) Eventually, water starts to leak in and gradually fills the car. What is the mass of the water that entered the car when the car starts to sinks? Density of water is 1000 kg/m3.

Question

Physics

Angelique Duke

2 February, 22:43

While driving his 600-kg ultra-compact electric car, a distracted driver starts crossing a drawbridge. Not realizing that the drawbridge is about to open, he ends up in the river below with his car. Fortunately the car stayed afloat for a while and he is able to escape before it starts sinking. (a) If the volume of the interior is 2.0 m3, what fraction of the car is immersed while it floats? (b) Eventually, water starts to leak in and gradually fills the car. What is the mass of the water that entered the car when the car starts to sinks? Density of water is 1000 kg/m3.

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Diamond · Answer 1

a)

weight of car = 600 kg.

According to Archimedes principle, for free floatation,

weight of car = weight of displaced water

600 x 9.8 = v x 10³ x 9.8, v is volume of water displaced and 10³ kg / m³ is density of water.

v =.6 m³

required fraction

=.6 / 2

=.3

b)

Let mass of water entering before the start of sinking of car.

mass of maximum displaced volume of water by car = 2 x 10³m³.

(600 + m) x g = 2 x 10³ x g [ 10³ is density of water ]

600 + m = 2000

m = 1400 kg.