Final answer:
The force exerted by water on the dam can be found using the formula F = pgh²L/2, and with the provided dimensions and water density,
So, the correct answer is:
a. 2,588,320 lb
Step-by-step explanation:
The student has asked about the force exerted by water on a rectangular dam. To calculate this force, we use the formula F = pgh²L/2, where p is the density of water, g is gravitational acceleration, h is the depth of the water at the dam, and L is the length of the dam.
Given that the water is 40 ft deep, the dam is 103 ft long, and the density of water is 62.4 lb/ft³, we substitute these values into the formula to get F = (62.4 lb/ft³)(32.2 ft/s²)(40 ft)²(103 ft)/2, which calculates to 1,544,320 lb. This results in option b being the correct answer.
To calculate the force exerted by water on a rectangular dam, we can use the formula F = pgh²L/2, where p is the density of water, h is the depth at the dam, and L is the length of the dam. In this case, the density of water is given as 62.4 lb/ft³.
The depth at the dam is 40 ft, and the length of the dam is 103 ft. Plugging in these values, we get F = (62.4 lb/ft³)(40 ft)(40 ft)(103 ft)/2 = 2,588,320 lb. Therefore, the force exerted by the water on the dam is 2,588,320 lb, which corresponds to option a.