Exam1-TTh

Exam1-TTh -

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Unformatted text preview: NAME: Exam One:Tuesday/Thursday Class September 25, 2009 1. (30 Points) RECTILINEAR MOTION SCORE: AME 301: Fall 2009 D. C. Wilcox The acceleration of sliding block A is a = -v/ , where is a constant time scale. When the block begins its motion at time t = 0, its position and velocity are given by x = and v = vo . As t , we observe that x 3 . Determine vo . 2 . ..... ..... ... ....... . ... ..... ... ..... .... ... ...... ... ... .... ............ ... .... ............ . .. ... ... ... ... ... .. .. ... ... ... ... ... ... ..... ... ..... ... ... . ... ... . ... ... ... ... ... .. ... .. ... ... ... ... ... ..... ... ..... . ... ... ... ... ... ... ... ... ... .... ... ... . ... ... ... ... ... ... ... .... . ... ... ... ... ... .. ... .... . ... .......................... ... ................. ........ ... .. ... ......................................... . . . . ... ... ...... ... ..... ... ...................................... . . . ... ....................................... . ... ..... . . . . . ... .. ... ..... ... ................................. .................. .. . . . . . ................... .... ....... .............................. ......... ... . .. ........... ..... .......... ............................. ............... ........ ... . ..... . . . . ....... . .. . ..... ..................... . . ........... ........ ............. ...... . . . . . .. . . ............ ..... ...... ... ............. . ................. ................... ............ ............ . . .. . .............. .. . . . . . . . . ........................... ............................................. . .. . . . . ............................ ............................................. .. . . . . . . . ..... . . . . ........................... .............................................. ........................... ............................................... . . . . . . . . . . . . . ........................... .............................................. ........................... ............................................... . . . . . ............. ... ......................... .................... ................................................................................................................................................................................................................................................................................................................ . .... .... ... . . . . . . . . . . . .. . ............................................ ..................................................................................... . .. . ................................................................................................................................................................................................................................................................... .............................................................................................................. . . ............................................................................................................... ...................................................... . ................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................... .............................................................................................................................................................................................. . . . . . . ......................... . . ............................ . .. ... . . . . . . . . . . . ... . . . . .. . . . . . . . . . . ... . . ... ..... . .. . ... . ....................... ....... . .. ...................................... ....................................... .. . . .. . . ..................................... ...................................... . . . A x 2. (30 Points) RELATIVE MOTION OF TWO OBJECTS A ball is launched with speed V at an angle to the vertical at time t = 0 from a cart whose velocity is vA = (U - at) i, where U and a are constant. Determine the angle for which the ball will land at the same point from which it is launched. Express your answer as a function of a and gravitational acceleration, g. y y V O x A .. ... ..... . ...... . ..... . ..... ........... . ... ........................................................................ ................... ............................. ................................ . ................. ... ..... ... ........................................................................................................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................................................................................................................................ .. ..... ................................................................... . . . .................... .................................................................... . .................. . ........ ....................................................... . ................. ..... .. . . . . . .. . . . .. . . . . . . .. . .. . .. . .. t r f r x f 1 3. (40 Points) MOTION WITH CYLINDRICAL SYMMETRY A small sphere of mass m has a tangential speed V as it arrives at the top of a frictionless cylindrical surface of radius R. At time t = 0, the sphere continues sliding along the surface. At an angle s where the normal reaction force between the sphere and cylinder, N , is zero, the sphere separates from the surface. (a) State the equations governing the motion up to the separation point in cylindrical coordinates. Let g denote the acceleration of gravity. (b) Multiply the equation for the circumferential motion by and verify that V 2 2g 2 = 2 + (1 - cos ) R R (c) Using the result for 2 from Part (b), solve for N as a function of m, V , g and cos . (d) If the separation angle is s = cos-1 ( 5 ), what is V 2 /(gR)? 6 . . . . . . . . . . . . . . . . ... ... .. . .. .. . . ... .............. . . ... .. ............... . ..... . . . .. . . .. ........ ...... . . ........................ .. .................................... .......... . . ...... ........... ...................... . . ........................................................... . . ......................................................................... .......................................................................... . . .................................................................................. . .. . . . . . . . . ....................................................................................... . . ............ .... . ......................................................................................... .. . . ... . .. .. . ..... ....... . ............................................................................................ .. . ........ . ...... . ... . ... .. ... . .. ... ........................................................................................................ .. . .......................................................................................................... . ... . ...... ...... . ......... ... ........................................................................................................... .. .. . .... ........................................................................................................ ... ................................................................................................ ........................................................................................................... . . . ... .. .. .. . . .......... . ... .. . . ................................................................................................... . . .. . . .. . .................................................................................................................... . . ... . ................................................................................................................... . . ...... . . . .................................................................................................. . . ....................................................................................................................................................................................................................................................................... ... . . . . . . .... . ........................... ........................................................................................................................................................................................................... V v g R v R ............................................................................................................................................................................................................... ............................... . . ............................................................... . . . . ............................................................................................................................................................................................................... ............................................................................................................................................................................................................... v 2 ...
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