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Question

When cracks form at the base of a dam, the water seeping into the cracks exerts a buoyant force that tends to lift the dam. As a result, the dam can topple. Estimate the buoyant force exerted on a 2.0m thick by 4.0m wide dam wall by water seeping into cracks at its base. The water level in the lake is 5.0 m above the cracks.

A

1.09 X 105 N

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B

2.8 X 105 N

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C

3.9 X 105 N

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D

4.5 X 105 N

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Solution

The correct option is C 3.9 X 105 NThe buoyant force acting on the dam is given by Archimedes' principle: B = Wdisplaced water = mdisplaced water g =ρwaterVdisplaced water g The volume of the displaced water is the same as the volume of the dam: B = ρwaterVdamg = ρwater L W H g Where L, W, and H are the length and width of the dam, and H is the height of the water above the cracks. B=(1.00×103kg/m3)(2.0m)(4.0m)(5.0m)(9.81m/s2)=3.9×105N

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