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A dam is used to hold back a river. The dam has a height H=12m and a width W=10m. Assume that the density of the water is rho=1000kg/m³. (a) Determine the net force on the dam. (b) Why does the thickness of the dam increase with depth?

a) 1.2 MN, Buoyancy force
b) 1.8 MN, Buoyancy force
c) 2.4 MN, Gravitational force
d) 3.0 MN, Gravitational force

User Kayshawn
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Final answer:

The net force on the dam is 1.2 MN and it is due to the buoyancy force. The thickness of the dam increases with depth to balance the increasing force due to the increasing pressure.

Step-by-step explanation:

The net force on the dam can be determined by considering the buoyancy force acting on it. The buoyancy force is equal to the weight of the water displaced by the dam. The formula for the buoyancy force is FB = ρVg, where ρ is the density of water, V is the volume of the dam below the water level, and g is the acceleration due to gravity.

To determine the net force, you need to calculate the volume of the dam below the water level. The volume can be calculated using the formula V = A×H, where A is the area of the dam and H is the height of the dam. In this case, A = W×H, where W is the width of the dam.

Substituting the values into the formulas, the net force on the dam is Fnet = ρ(W×H×H)g = 1000 kg/m³ × (10 m × 12 m × 12 m) × 9.8 m/s² = 1.2 MN.

Answer: (a) 1.2 MN, Buoyancy force.

The thickness of the dam increases with depth to balance the increasing force due to the increasing pressure. The pressure at a given depth in a fluid is directly proportional to the depth. As the depth of the water increases, the pressure on the dam also increases. To counteract this increased pressure, the dam needs to have a thicker design to withstand the additional force.

Answer: (b) Buoyancy force.

User Pogrindis
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