Question

A crate with dimensions of 2.00 m × 3.00 m × 5.00 m is immersed in sea water (r = 1.025 × 103 kg/m3) with the 3.00 × 2.00 sides as the top and bottom. The crate is held with a cable so that the top is 20.0 m below the surface of the water.
a. Calculate the hydrostatic pressure on the top of the crate and on the bottom of the crate.

b. Find the absolute pressure at the top and at the bottom of the crate. (P0 = 1.01 × 105 N/m2)

c. Find the forces exerted on the top and on the bottom of the crate by these pressures.

d. On the diagram on the next page, sketch in vectors representing the direction and magnitude of these forces.

e. What is the net force exerted by the water on the crate?

f. The crate’s weight is 2.50 × 106 N. Will it sink when the cable is cut? Explain.

g. Calculate the volume of the crate.

h. Use Archimedes’ principle to find the buoyant force on the crate. How is it related to your answer to item e?

Answer 1

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