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plank laced cent across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (1) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and (iv) clear, logical, and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results. (b) Using the results you have obtained in part (a) (iv) above, explain whether the acceleration of the plank changes as the system moves so that the plank is no longer in the central position.

plank laced cent across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (1) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and (iv) clear, logical, and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results. (b) Using the results you have obtained in part (a) (iv) above, explain whether the acceleration of the plank changes as the system moves so that the plank is no longer in the central position.

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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Question A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (1) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and (iv) clear, logical, and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results. (b) Using the results you have obtained in part (a) (iv) above, explain whether the acceleration of the plank changes as the system moves so that the plank is no longer in the central position. + Keny
Transcribed Image Text:Question A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (1) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and (iv) clear, logical, and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results. (b) Using the results you have obtained in part (a) (iv) above, explain whether the acceleration of the plank changes as the system moves so that the plank is no longer in the central position. + Keny
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Would the plank and the roller have the same acceleration why or why not?

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