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To simplify this mechanical process, consider the following diagram (Figure 2). The location of the piston is represented by the point P. Suppose the crank has a circular rotation radius of r = 23 cm (distance from the origin to point A). The connecting rod (line AP) has a length of 40 cm. The rotation occurs counterclockwise, as increases through positive values at a rate of 360 revolutions per minute. The angle between line AP and the x-axis is represented by a (alpha). a) Find the angular velocity of the connecting rod, that is find 8 = radians. da dt a P(x,0) Figure 2 ,in radians per second, when Hint: Use the law of sines to help build a formula involving the two angles and two known sides, then differentiate implicitly. Also note that is given in revolutions per minute, this needs to be converted to radians per second. de dt It is important to calculate the forces exerted on the piston as the crank rotates. The forces produced are determined by the linear speed at which P travels along the x-axis. To calculate this speed, the distance x must first be determined, and then can be computed. dx dt b) Express the distance x as a function of 9. In other words, find the length of the line segment OP (from the origin to point P) as a function of 8 for r = 23 cm and IAPI = 40cm. Hint: Use the law of cosines to relate x and 9, the equation will be quadratic which you must solve for x.

To simplify this mechanical process, consider the following diagram (Figure 2). The location of the piston is represented by the point P. Suppose the crank has a circular rotation radius of r = 23 cm (distance from the origin to point A). The connecting rod (line AP) has a length of 40 cm. The rotation occurs counterclockwise, as increases through positive values at a rate of 360 revolutions per minute. The angle between line AP and the x-axis is represented by a (alpha). a) Find the angular velocity of the connecting rod, that is find 8 = radians. da dt a P(x,0) Figure 2 ,in radians per second, when Hint: Use the law of sines to help build a formula involving the two angles and two known sides, then differentiate implicitly. Also note that is given in revolutions per minute, this needs to be converted to radians per second. de dt It is important to calculate the forces exerted on the piston as the crank rotates. The forces produced are determined by the linear speed at which P travels along the x-axis. To calculate this speed, the distance x must first be determined, and then can be computed. dx dt b) Express the distance x as a function of 9. In other words, find the length of the line segment OP (from the origin to point P) as a function of 8 for r = 23 cm and IAPI = 40cm. Hint: Use the law of cosines to relate x and 9, the equation will be quadratic which you must solve for x.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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To simplify this mechanical process, consider the following diagram (Figure 2). The location of the piston is represented by the point P. Suppose the crank has a circular rotation radius of r = 23 cm (distance from the origin to point A). The connecting rod (line AP) has a length of 40 cm. The rotation occurs counterclockwise, as increases through positive values at a rate of 360 revolutions per minute. The angle between line AP and the x-axis is represented by a (alpha). a) Find the angular velocity of the connecting rod, that is find 8 = radians. da dt a P(x,0) Figure 2 , in radians per second, when Hint: Use the law of sines to help build a formula involving the two angles and two known sides, then differentiate implicitly. Also note that is given in revolutions per minute, this needs to be converted to radians per second. de dt It is important to calculate the forces exerted on the piston as the crank rotates. The forces produced are determined by the linear speed at which P travels along the x-axis. To calculate this speed, the distance x must first be determined, and then can be computed. dx dt b) Express the distance x as a function of 0. In other words, find the length of the line segment OP (from the origin to point P) as a function of for r = 23 cm and IAPI = 40cm. Hint: Use the law of cosines to relatex and 0, the equation will be quadratic which you must solve for x.
Transcribed Image Text:To simplify this mechanical process, consider the following diagram (Figure 2). The location of the piston is represented by the point P. Suppose the crank has a circular rotation radius of r = 23 cm (distance from the origin to point A). The connecting rod (line AP) has a length of 40 cm. The rotation occurs counterclockwise, as increases through positive values at a rate of 360 revolutions per minute. The angle between line AP and the x-axis is represented by a (alpha). a) Find the angular velocity of the connecting rod, that is find 8 = radians. da dt a P(x,0) Figure 2 , in radians per second, when Hint: Use the law of sines to help build a formula involving the two angles and two known sides, then differentiate implicitly. Also note that is given in revolutions per minute, this needs to be converted to radians per second. de dt It is important to calculate the forces exerted on the piston as the crank rotates. The forces produced are determined by the linear speed at which P travels along the x-axis. To calculate this speed, the distance x must first be determined, and then can be computed. dx dt b) Express the distance x as a function of 0. In other words, find the length of the line segment OP (from the origin to point P) as a function of for r = 23 cm and IAPI = 40cm. Hint: Use the law of cosines to relatex and 0, the equation will be quadratic which you must solve for x.
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