Midterm_Solution-1

# Midterm_Solution-1 - Question 1 Rod AB of length l and...

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Question 1) Rod AB of length “l” and negligible weight lies in a vertical plane and is pinned to blocks A and B. The weight of each block is W, and the blocks are connected by an elastic cord which passes over a pulley at C. Neglecting friction between the blocks and the guides, determine the value of as a ! function of the tension in the cord, T (known). Using cos(a+b) = cos(a)cos(b) – sin(a)sin(b) sin(a+b) = sin(a)cos(b) + cos(b)sin(a) W*(cos( )cos(60) – sin( )sin(60)) + T*(sin( )cos(30) + cos( )sin(30) – cos( )cos(30) + ! ! ! ! ! sin( )sin(30)) = 0 ! ! ! -W*tan( )sin(60) + T*tan( )*(cos(30) + sin(30)) + W*cos(60) + T*(sin(30) – ! ! cos(30)) = 0 ! tan( )(-W*sin(60) + T*(cos(30)+sin(30)) = T*(cos(30) – sin(30)) – W*cos(60) ! ! = tan ! -1 (T*(cos(30) – sin(30)) – W*cos(60) ) = tan -1 (T*(1 – sqrt(3)) – W) -W*sin(60) + T*(cos(30)+sin(30)) (-W*sqrt(3) – T*(sqrt(3) +1)

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