Consider a semicircular dam with a radius of 40 feet. 1. Suppose that the flat edge...

Transcribed Image Text:

Consider a semicircular dam with a radius of 40 feet. 1. Suppose that the flat edge of the semicircle is at the surface of the water and the rounded edge is submerged below the surface. Assume water density is 62.4 lb/ft Determine the total force exerted by the water against the surface of the dam. Your solution should include: a drawing of the surface of the dam the xy axis you are using, clearly indicating both direction and positive or negative sign clear indication of the water level on your drawing coordinates of any points impacting the problem the expression you are using for the depth of the water with the process used to determine this the expression you are using to represent the width of one slice of the dam with the process used to determine this the integral which will be used for calculating the total force steps used to evaluate the integral, with proper notation the final answer, written in a complete sentence. 2. For the same semicircular dam, suppose that the water rises to within 4 feet of the top of the dam rather than having the flat edge at the surface of the water. (That is, the water level is below the top of the dam.) Set up the corresponding integral to determine the total force exerted by the water against the surface of the dam. DO NOT EVALUATE THE INTEGRAL. Consider a semicircular dam with a radius of 40 feet. 1. Suppose that the flat edge of the semicircle is at the surface of the water and the rounded edge is submerged below the surface. Assume water density is 62.4 lb/ft Determine the total force exerted by the water against the surface of the dam. Your solution should include: a drawing of the surface of the dam the xy axis you are using, clearly indicating both direction and positive or negative sign clear indication of the water level on your drawing coordinates of any points impacting the problem the expression you are using for the depth of the water with the process used to determine this the expression you are using to represent the width of one slice of the dam with the process used to determine this the integral which will be used for calculating the total force steps used to evaluate the integral, with proper notation the final answer, written in a complete sentence. 2. For the same semicircular dam, suppose that the water rises to within 4 feet of the top of the dam rather than having the flat edge at the surface of the water. (That is, the water level is below the top of the dam.) Set up the corresponding integral to determine the total force exerted by the water against the surface of the dam. DO NOT EVALUATE THE INTEGRAL.