A 9.6 kg block of metal is suspended from a scale and immersed in water, as in t

Question

A 9.6 kg block of metal is suspended from a scale and immersed in water, as in the figure below. The dimensions of the block are 12.0 cm 12.0 cm 12.0 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 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 = 1.0130 105 N/m2. Ftop Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. N Fbottom N (b) What is the reading of the spring scale? Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block. (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

P(h) = gh + P0

P(.05m) = 9800N/m³ * .05m + 1.013e5 N/m² = 1.0179e5 Pa
Ftop = P(.05)*A = 1.0179e5*(0.12²m²) = 1465.776 N

P(.17m) = 9800N/m³ * 0.17m + 1.013e5 N/m² = 1.02966e5 Pa
Fbottom = P(0.17)*A = 1.02966e5*(.12²m²) = 1482.71 N

Reading
mg +Ftop - Fbottom = 77.14 N

Also
9.6*9.8 - 9800N/m³ * (.12*.12*.12)m³ = 77.14 N

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