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Gil is a perfectly spherical fish bred specifically for use in physics problems. Gil has mass of 33.5 kg. By inflating/deflating his air bladder, Gil has the ability to change his volume while his mass does not change appreciably. Gil sleeps in a small cylinder chamber. The small chamber is connected to a larger chamber by a tapering passageway. The walls of the containers are made of aluminium with a small glass window (diameter = 0.4 m) in the larger chamber. Both chambers are sealed by large (thin) weights that can move up/down as water levels change. Gil is initially 5 m from the bottom of the smaller cylinder.

Part A: Both tanks are filled with water (p=1000 kg/m^3). The small weight has a mass of 10,000 kg and radius of 2 m. The large weight has mass of 2,000,000 kg and radius of 10m. If the water is 15 m from the floor, what is the water level in the larger cylinder? The system is in equilibrium.

**I get 9.03 m**

Part B: Gil adjusts his position in the tank by adjusting his bladder (and thus his volume). What must Gil's radius be to remain stationary in the water tank?

**I get 0.2 m**

Part C: Gil wants to rise to the top of the tank. If he doubles his radius, what will his resultant acceleration be? Ignore frictional effects.

**I get 68.6 m/s^2**

Part D: How long will it take Gil to strike the floating weight at the top of the tank? Ignore friction and turbulence. What will his speed be?

**I get .274 s and 18.8 m/s**

Part E: In order to conduct an experiment, a scientist wishes to force gil into the larger tank. She accomplishes this by adding an additional 63,000 kg of mass to the smaller cylinder.

*Qualitatively*describe the acceleration and velocity.

**I put: The velocity of the small disk will change until it and the acceleration will equal zero. The acceleration changes due to changes in Net Force by changes in pressure**

Part F: Calculate the initial accelerations of both the small and large weights at the moment the 63,000 kg mass is added. Are these values the same? Why or why not?

**I get 8.49 m/s^2 for small and .309 m/s^2 for large. No they are not same because they are spread over different areas**

Part G: What will the new water levels be once the system reaches equilibrium?

**i get 12.91 for small and 9.45 for large**

Part H: Gil is carried into large tank by flow of water. If he enters the large end of the passage (radius 2 m) with velocity of 3.2 m/s, with what velocity will he come out of the other end (radius .5 m)?

**I get 12.8 m/s**

There is more, but I like to know this part is right first before continuing...