Archimedes' principle - Acceleration of an anchor

Problem statement:

If an anchor is made of iron, find its acceleration when it sinks after being dropped in the sea.

Givens: ρfl = 1.03 103 kg/m3; ρFe = 7.85 103 kg/m3; g = 10 m/s2

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Solution:

To solve this problem we are going to apply Archimedes’s principle as well as Newton’s second law.

In the figure below the forces acting on the anchor, its weigh P and the buoyant force F are shown:

Using Newton’s second law:

Since the density of iron is greater than the density of sea water, the magnitude of the anchor’s weight is greater than the magnitude of the buoyant force, so the acceleration of the anchor points downwards. Projecting onto the vertical axis:

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According to Archimedes’ principle, the magnitude of the buoyant force is equal to the weight of the water displaced by the anchor. Also, we can calculate the mass of the anchor as a function of its density . Since the anchor is completely immersed in water, the volume of the displaced fluid is equal to the volume of the anchor. Substituting the givens:

Make sure that you include units in your results.

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