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Dynamics_Part12

# Dynamics_Part12 -

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Unformatted text preview: Problem Set 2: Problem 2. Problem: At time t = 0, Block A begins sliding down an incline of angle with constant acceleration a and Block B begins moving to the right with constant acceleration 5 a relative to Block A. Determine the 4 absolute acceleration of Block B, aB and its speed, |vB |, as a function of a, t and . If the acceleration of Block A is a = 10 cm/sec2 and = 30o , what is |vB | when t = 5 sec? y . .. .................. .... .. . . .. . ............ . ............. ... . ................. .. ................... .................... ...................... . . . .. .. .................... .. ...................... . .. . ................. ..................... . ...................... . . . ...................... . .................. . ...... ........ ................ ...................... . .................... ..................... . . ..................... . . .. .... .... ............ . . ............................................ ............................... ............... .... .............. .... . . .............................................. ............................ . . .. ..... .. . . . . .................. .... .. .. . ........ ..... ..... ............. .. . . . . . ..................... ........ ....................... . . ................ .. . . .......................... . . .... ....... ... . .. ................... ....................... .................... . . .............................. . . . ... . ..... . ...... .. ...... .................... ....................... ........................................ . . .................................. . . . ... .. . ... . ............... ............................................ .. .............................. . . .................. .. ................................................................................... ................................................. .......................... . .. . . .. .... .. ... .. ............................................................................ . . .............................................................................. . . . .. . . ................ .. ........................................................................ . . .......................................................................................................... . . . ................................................................................................................. . . .... ............ ........ . .... . . .................................................................................... . . ................................................................................................... . . . ... . . ................................................................................................. . .. ........ ........ ....... . . .......................................... ............................... . . ....................................................................................... .. . . ... ... ... . . .... ... . .................................................................................................. .......................................................................... . . .. . . . . .......... . ... . . . ... ....................... . . .. . . . ................................................... ............................................................ . ... ... ...... . . .... ......... ..... . .. ................. ...................... . . .............. .................... . ... . ....... ............. ....................... . . ............................. .. . .... . .. .. . . .......................... . . ... ........ ..... . . ......... ................. ................................... .................................................................. . ... ...... . .. .................................................................................................. .......... .......... .. . .. . . .. . .. ... B A x Also, Block B's acceleration vector, relative to Block A, is aB/A = Thus, the absolute acceleration of Block B is Solution: Since Block A slides down the incline, its acceleration vector is tangent to the incline. Hence, we conclude that aA = a(-i cos - j sin ) 5 ai 4 5 aB = aA + aB/A = a(-i cos - j sin ) + a i 4 Rearranging terms, we find 5 - cos a i - a sin j 4 Thus, since the velocity vector is vB = aB t, the speed at time t is aB = |vB | = at = at = at = at Therefore, Block B's speed at time t is |vB | = at 4 41 - 40 cos 5 - cos 4 2 + sin2 25 5 - cos + cos2 + sin2 16 2 25 5 - cos + 1 16 2 41 5 - cos 16 2 We are given a = 10 cm/sec2 and = 30o , what is |vB | when t = 5 sec. Substituting into the equation above, we have the following. 1 cm cm (5 sec) 41 - 40 cos 30o = 31.5 10 |vB | = 2 4 sec sec ...
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