Lurking alligators. An alligator waits for prey by floating with only the top of
ID: 1399449 • Letter: L
Question
Lurking alligators. An alligator waits for prey by floating with only the top of its head exposed, so that the prey cannot easily see it. One way it can adjust the extent of sinking is by controlling the size of its lungs. Another way may be by swallowing stones (gastrolithes) that then reside in the stomach. The figure shows a highly simplified model (a ''rhombohedron gater'') of mass 130 kg that roams with its head partially exposed.The top head surface has area 0.310 m2. If the alligator were to swallow stones with a total mass of 1.4% of its body mass (a typical amount), how far (in mm) would it sink?
Explanation / Answer
let the height alligator sink is h
area of cross section , A = 0.310 m^2
mass of stones swallowed , m = 1.4 * 140/100
m = 1.96 Kg
Now, for floating ,
weight of swallowed stones = weight of extra water displaced
1.96 * 9.8 = 0.310 * h * 1000 * 9.8
solving for h
h = 6.322 *10^-3 m
the alligotar will sink 6.322 *10^-3 m after swallowing the stones
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