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You are part of a team of astronauts whose job is to move a meteor, so it doesn't crash into Earth. NASA has designed rockets to push the meteor, but they can only push perpendicular to the surface of the meteor where they come in contact. You are piloting rocket #1 and it's your job to keep the meteor from starting to spin.

You are part of a team of astronauts whose job is to move a meteor, so it doesn't crash into Earth. NASA has designed rockets to push the meteor, but they can only push perpendicular to the surface of the meteor where they come in contact. You are piloting rocket #1 and it's your job to keep the meteor from starting to spin.

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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A, B, and C
3. You are part of a team of astronauts whose job is to move a meteor, so it doesn't crash into Earth. NASA has designed rockets to push the meteor, but they can only push perpendicular to the surface of the meteor where they come in contact. You are piloting rocket #1 and it's your job to keep the meteor from starting to spin. 180° С.О.М. a. Find the torque from Fm about the center of mass in terms of F 2,vř,vi and 0. Simplify your answer as much as possible. (Note that i, points along the x axis.) b. Find the torque from F about the center of mass using the vector cross product, assuming that: i,=x, &+ y,ŷ F, 3m=F3m.xâ+F3m. vŷ C. The surface that rocket #4 is pushing on is parallel to the y axis. Find the vector component of that is perpendicular to Fm which is the "lever arm" for this force. Then use that to find the torque from F, about the center of mass of the meteor in terms of ¿ F Vi, iřvi and ø. 4m 4m d. Find the angle that F makes with ř5. Use this angle to find the torque from Fabout the center of mass of the meteor in terms of i F V,vř| and the angle you solved for. Use the appropriate trig '5m identity to simplify the result. e. Find the torques about the center of mass of the meteor from rockets 6 and 7 in terms of the magnitudes of the forces and the magnitudes of the position vectors. You have a special ship that grapples to the surface of the asteroid and can push or pull. To keep the asteroid from starting to rotate, the torques from all the rockets (including yours) must add up to zero. f. Assuming your rockets is pulling, solve for the magnitude of the force must you apply in terms of the answers from all the other parts, iř,Vi, and the angles shown in the diagram.
Transcribed Image Text:3. You are part of a team of astronauts whose job is to move a meteor, so it doesn't crash into Earth. NASA has designed rockets to push the meteor, but they can only push perpendicular to the surface of the meteor where they come in contact. You are piloting rocket #1 and it's your job to keep the meteor from starting to spin. 180° С.О.М. a. Find the torque from Fm about the center of mass in terms of F 2,vř,vi and 0. Simplify your answer as much as possible. (Note that i, points along the x axis.) b. Find the torque from F about the center of mass using the vector cross product, assuming that: i,=x, &+ y,ŷ F, 3m=F3m.xâ+F3m. vŷ C. The surface that rocket #4 is pushing on is parallel to the y axis. Find the vector component of that is perpendicular to Fm which is the "lever arm" for this force. Then use that to find the torque from F, about the center of mass of the meteor in terms of ¿ F Vi, iřvi and ø. 4m 4m d. Find the angle that F makes with ř5. Use this angle to find the torque from Fabout the center of mass of the meteor in terms of i F V,vř| and the angle you solved for. Use the appropriate trig '5m identity to simplify the result. e. Find the torques about the center of mass of the meteor from rockets 6 and 7 in terms of the magnitudes of the forces and the magnitudes of the position vectors. You have a special ship that grapples to the surface of the asteroid and can push or pull. To keep the asteroid from starting to rotate, the torques from all the rockets (including yours) must add up to zero. f. Assuming your rockets is pulling, solve for the magnitude of the force must you apply in terms of the answers from all the other parts, iř,Vi, and the angles shown in the diagram.
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