1. A storage tank of negligible mass and 30m high is filled with gasoline. Pleas

Question

1. A storage tank of negligible mass and 30m high is filled with gasoline. Please calculate the following:

(a) The gauge pressure and absolute pressure at the bottom of the tank. 4 pts
(b) The force that acts on a square access hatch at the bottom of the tank that measures 0.5m x 0.5m. 2 pts
(c) Given that the tank is shaped like a right circular cylinder with a height of 30 m and with a base radius of 10m. The tank is attached to a steel cable of negligible mass and immersed in water. Calculate the tension (force) in the cable before and after it is immersed in water. 4 pts





2. A blimp used for aerial camera views of sporting events holds 200,000 ft3 of helium.

a) How much does the helium weigh? 3 pts

b) What is the buoyant force on the blimp at sea level? 3 pts

c) How much can the blimp lift in addition to the helium? 4 pts



3. A box-shaped piece of concrete measures 3ft by 2ft by 0.5ft.

a) What is its weight? 3 pts

b) Find the buoyancy force that acts on it when it is submerged in water. 3pts

c) What is the net force on the concrete piece when it is under water? 4pts



4. A Styrofoam slab has thickness h and density ?s . When a swimmer of mass m is resting on it, the slab floats in fresh water with its top at the same level as the water surface. Find the area of the slab. 10 pts





5. A thin spherical shell of mass 4.00 kg and diameter 0.200 m is filled with helium (density ? = 0.180 kg/m3). It is then released from rest on the bottom of a pool of water that is 4.00 m deep. (a) Neglecting frictional effects, show that the shell rises with constant acceleration and determine the value of that acceleration. 5pts (b) How long will it take for the top of the shell to reach the water surface? 5 pts

Explanation / Answer

1.

a)

dencity of gasoline = = 700 kg/m3

gauge pressure = g h = 700 * 9.8 * 30 = 205800 Pa

absolute pressure = 205800 + 1.013e5 = 307100 Pa

b)

F = P A = 307100 * (0.5*0.5) = 76775 N

c)

before >>>>> T = (L R2) g = 700*30*3.14*10*10*9.8 = 64621200 N

after >>>> gasoline < water >>>>> T = 0

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