Question

A trough has a parabolic cross section y = ax^2, where a is a constant. The height is H meters and the length is L meters. The trough is filled with water. For this problem, approximate the weight density of water to be rhog = 10^4 Newtons per cubic meter.

A) True
B) False

Answer 1

The total force on a rectangular dam due to water is calculated with the equation F = pgh²L/2 and is proportional to the depth of the water squared and the length of the dam.

Step-by-step explanation:

The total force on a rectangular dam due to the water behind it is directly proportional to the depth of the water squared and the length of the dam. This force can be calculated using the formula F = pgh²L/2, where p is the density of water, g is the acceleration due to gravity (9.8 m/s²), h is the depth of water at the dam, and L is the length of the dam. By calculating the average pressure (which is pgh/2 since pressure increases linearly with depth) exerted by the water on the dam and multiplying it by the area in contact with the water (which is hL), we can obtain the force exerted on the dam by the water. When the water density is known and the depth is given, for instance, an average depth of 40.0 meters, these values can be substituted into the equation to calculate the force.