1. A U-shaped tube is partially filled with water. One side of the tube is attac

Question

1. A U-shaped tube is partially filled with water. One side of the tube is attached to a glass bulb while the other is open to atmosphere. What is the pressure inside the bulb if the water level on the side exposed to atmosphere is 12.0 cm lower than that of the side attached to the bulb?

2. A cube of iron with sides 10.1 cm long is glued to the center of the top of a cube of wood with sides 0.270m long. The mass of the two blocks glued together is 12.0 kg. The two blocks are placed in fresh water. What fraction of the wood block's volume must be submerged for the blocks to float if (a) the wood is on the bottom and if (b) the iron block is on the bottom?

I know the answer to 1 is P=99.8 kPa and 2 is V (for wood)=0.610 and V (for iron)= 0.557 but I do not know how to work them. Please help!

Explanation / Answer

1) P + row*g*h + row*v^2 /2   = constant

so deltaP = row*g*deltaH

101325 Pa -   P   = 1000 kg/m^3 * 9.81 m/s^2 * 0.12m

P = 100147.8 Pa

2) volume of wood Vw = 0.270^3 = 0.0197 m^3

volume of iron Vi = 0.101^3 = 1.03 x 10^-3 m^3

density of iron di = 7850 kg/ m^3

a) when wood is in bottom,

Fb = buoyant force = volume of water displaced x density of water x g

balancing forces,

Fb = mg

V x 1000 x 9.81 = 12 x 9.81

(0.270^2 x h1 ) = 12 /1000

h1 =   0.165 m

fraction = Vsubmerged / Vtotal = (L^2 x h1 ) / L^3 = 0.165 / 0.270 = 0.61

b) when iron block is at bottom,

(1.03 x 10^-3   + V ) x 1000 x 9.81 = 12 x 9.81

(1.03 x 10^-3   + V ) = 0.012

V = 0.270^2 x h2 = 0.01097

h2 = 0.15 m

fraction = 0.15 / 0.27 = 0.55

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