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(c9p30) A 1.93 -kg block of metal is suspended from a scale and immersed in wate

ID: 2191009 • Letter: #

Question

(c9p30) A 1.93 -kg block of metal is suspended from a scale and immersed in water as in Figure P9.30. The dimensions of the block are 8.0 cm x 6.0 cm x 6.0 cm. The 8.0-cm dimension is vertical, and the top of the block is 9.0 cm below the surface of the water.

(a) What are the forces exerted by the water on the top and bottom of the block? (Take P0 = 1.013?105 N/m2.) (top force, bottom force)

(b) What is the reading of the spring scale?

(c) Notice that the buoyant force equals the difference between the forces at the top and bottom of the block. What is the buoyant force?

Explanation / Answer

Area = 6*6 = 36 cm^2

a) Pressure on top surface = gh = 1000*9.81*(9/100) = 883 Pa

Total pressure on top surface = 1.013*10^5 + 883 = 102183 Pa

Force on top surface = 102183*(36*10^-4) = 367.8 N

Pressure on bottom surface = gH = 1000*9.81*(9+8)/100 = 1667.7 Pa

Total pressure on bottom surface = 1.013*10^5 + 1667.7 = 102967.7 Pa

total force on bottm surface = 102967.7*36*10^-4 = 370.7 N

b)

Reading of spring scale = 1.93*9.81 - (370.7 - 367.8) = 16 N

c) Difference between top and bottm forces of block = 370.7 - 367.8 = 2.9 N

Buoyant force on bottom surface = (8*6*6)*1000*9.81/10^6 = 2.825 N