Question 2: A point-mass M of mass m is tied to a string which winds around a cylinder like a bobbin. The string is pinned on the cylinder at some point, and P denotes the point at which the string leaves the bobbin and starting from which it is taut. The cylinder has radius a and rotates at a constant rate around the vertical axis of the fixed frame F (which is also the axis of symmetry of the bobbin). The motion takes place in the hori- zontal plane, which is assumed frictionless. See figure. (a) Find a relationship between l, a and expressing that the length of the string is constant (b) Compute the velocity and acceleration of point M with respect to F. (c) Apply LMB in F to the system consisting of the point mass M alone (don't forget to start with a free body diagram!). Deduce a differential equation for l as well as the value of the string's tension in terms of the other parameters. (d) (bonus) Solve the differential equation for l.

Question 2: A point-mass M of mass m is tied to a string which winds around a cylinder like a bobbin. The string is pinned on the cylinder at some point, and P denotes the point at which the string leaves the bobbin and starting from which it is taut. The cylinder has radius a and rotates at a constant rate around the vertical axis of the fixed frame F (which is also the axis of symmetry of the bobbin). The motion takes place in the hori- zontal plane, which is assumed frictionless. See figure. (a) Find a relationship between l, a and expressing that the length of the string is constant (b) Compute the velocity and acceleration of point M with respect to F. (c) Apply LMB in F to the system consisting of the point mass M alone (don't forget to start with a free body diagram!). Deduce a differential equation for l as well as the value of the string's tension in terms of the other parameters. (d) (bonus) Solve the differential equation for l.

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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