Cartesian diver. A Cartesian diver is an inverted capsule with a small trapped a

Question

Cartesian diver.

A Cartesian diver is an inverted capsule with a small trapped air bubble. The diver is shown in Fig. 1 to be barely submerged in water. When the airtight flexible membrane covering the water container is pressed down, air pressure above the water increases. This pressure increase is transmitted to the water, which squeezes the trapped bubble to a smaller volume and thus letting more water into the capsule. This makes the capsule denser, accelerating it downward.

FIG. 1: Cartesian diver: an inverted capsule with a small trapped air bubble is barely submerged in water. When the airtight flexible membrane on the top of the container is pressed, the diver accelerates downward.

(a) Find the downward acceleration a of the diver if the total volume of the capsule is V , the initial volume of the trapped bubble is Vb V , and the compression of the membrane increases the air density in the bubble from 1 to 2.

(b) Compute a from part (a) if 1 = 2.4 kg/m3, 2 = 3.8 kg/m3, the capsule is a cylinder of length 7 cm and radius 0.5 cm, and initially the bubble is a sphere with 4 mm radius. (You may use a calculator.)

Explanation / Answer

as VbVb V-Vb=V b)V=0.07**0.005*0.005=5.49*10-6m3 Vb=4(0.004)3/3=2.68*10-7m3 2=3.8kg/m3   1=2.4kg/m*m*m    w=1000kg/m*m*m a=(3.8-2.4)2.68*10-7/5.49*10-3=6.83*10-5m/sec*sec

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