1) A cubical block of wood, 10.4 cm on a side, floats at the interface between o

Question

1) A cubical block of wood, 10.4 cm on a side, floats at the interface between oil and water with its lower surface 1.60 cm below the interface (the figure (Figure 1) ). The density of the oil is 790 kg/m3

a) What is the gauge pressure at the upper face of the block?

b) What is the gauge pressure at the lower face of the block?

c) What is the mass of the block?

d) What is the density of the block?

________________________

2) If the barge is made out of 4.9-cm -thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in freshwater without sinking?

Express your answer using two significant figures.

Explanation / Answer

1) (a) Pupper = rho g h
rho of oil = 790 Kg/m^3
g = 9.8
h = 1.60 cm = .016 m

P = 790 x 9.8 x .016

P(upper) = 123.872

(b) P(lower) = (rho)oil x g x h + (rho)water x g x h'

h = 10.4 cm = .104 m
h' = 1.60 cm = .016 m

P(lower) = (790 x 9.8 x .104) + (1000 x 9.8 x .016)

P(lower) = 961.968

(c) Weight = (P(lower) - P(upper)) x Area of block

Area (A) = (2Lb + 2bh + 2hL) = 2 (Lb + bh + hL) = 2 x ((40 x 22) +(22 x 12) + (12 x 40)) = 3248 m^2

W = (961.968 - 123.872) x 3248

W = 2722135.81 N

Mass = W / g

M = 2722135.81 / 9.8

Mass = 277768.96 Kg

(d) density of block
M = rho x Volume

rho = M / V

Volume = Lbh = 40 x 22 x 12 = 10560 m^3

rho = 277768.96 / 10560

rho = 26.3 Kg/m^3

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