Figure 1 shows a box of mass m that is supported on a surface inclined at angle 0 to the horizontal. The surface is covered with a thin layer of viscous oil that generates a resistance to any sliding movement of the box such that the resisting force is F =-qv, where v is the sliding velocity. At time t=0 the velocity of the box up the incline is v, . Figure 1 When the units of the drag force are [N] and the units of velocity are [m/sec], state the units of the coefficient q. (a) After a long time has passed, what will be the speed of the box? State clearly the principle that enabled you to obtain this result without solving the differential equation of motion. (b) (c) By counting the number of energy storage elements, what order do you expect the system dynamic equation to be? (d) Derive the differential equation governing the velocity of the box. (e) By inspection of your differential equation, state the system time constant. (f) Solve the differential equation derived in part (d) and hence determine an expression for the velocity of the box for t>0. including obtaining expressions

Figure 1 shows a box of mass m that is supported on a surface inclined at angle 0 to the horizontal. The surface is covered with a thin layer of viscous oil that generates a resistance to any sliding movement of the box such that the resisting force is F =-qv, where v is the sliding velocity. At time t=0 the velocity of the box up the incline is v, . Figure 1 When the units of the drag force are [N] and the units of velocity are [m/sec], state the units of the coefficient q. (a) After a long time has passed, what will be the speed of the box? State clearly the principle that enabled you to obtain this result without solving the differential equation of motion. (b) (c) By counting the number of energy storage elements, what order do you expect the system dynamic equation to be? (d) Derive the differential equation governing the velocity of the box. (e) By inspection of your differential equation, state the system time constant. (f) Solve the differential equation derived in part (d) and hence determine an expression for the velocity of the box for t>0. including obtaining expressions

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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