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
• B. 2.8 X 10⁵ N
• C. 3.9 X 10⁵ N
• D. 4.5 X 10⁵ N

Answer 1

The correct option is C

3.9 X 10⁵ N

The buoyant force acting on the dam is given by Archimedes' principle:

B = $W_{displacedwater}$ = $m_{displacedwater}$ g

$={\rho }_{water}{V}_{displacedwater}$ g
The volume of the displaced water is the same as the volume of the dam:

B = ${\rho }_{water}{V}_{dam}$g = ${\rho }_{water}$ 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.

$B=(1.00\times {10}^{3}kg/m^3)\left(2.0m\right)\left(4.0m\right)\left(5.0m\right)\left(9.81m/s^2\right)=3.9\times {10}^{5}N$