Solved: Modeling Data The hydraulic cylinder on a woodsplitter has a four-inch bore

Chapter 7, Problem 42

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Modeling Data The hydraulic cylinder on a woodsplitter has a four-inch bore (diameter) and a stroke of 2 feet. The hydraulic pump creates a maximum pressure of 2000 pounds per square inch. Therefore, the maximum force created by the cylinder is pounds. (a) Find the work done through one extension of the cylinder given that the maximum force is required. (b) The force exerted in splitting a piece of wood is variable. Measurements of the force obtained when a piece of wood was split are shown in the table. The variable measures the extension of the cylinder in feet, and is the force in pounds. Use Simpsons Rule to approximate the work done in splitting the piece of wood. (c) Use the regression capabilities of a graphing utility to finda fourth-degree polynomial model for the data. Plot the dataand graph the model.(d) Use the model in part (c) to approximate the extension ofthe cylinder when the force is maximum.(e) Use the model in part (c) to approximate the work done insplitting the piece of wood.