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. Block A (right-most block) travels downward with va = 3t^2 in the downward direction. Consider the following pulley system. Assume the length of the long rope L is constant, and is contact without slip with both pulleys. Assume that the length K of the right-most pulley is held a constant K. Assume the fixed frame basis is {i, j, k}, which is right-handed, where j is downward, and k is out of the paper.
A Define an equation for the length L in terms of the values given in the figure. This is known as a constraint equation. Hint: It may help you to identify which of these values are scalars and which remain constant.
B Provide kinematic equations for the position and velocity of the center of the left-most pulley (point C) in coordinates {i, j, k}.
C What is the velocity of block B (left-most block) when t = 3?
D Consider an intrinsic coordinate system {êt, én, és} for point E which is fixed to the long rope in this set-up. What are the directions of êt, én and és at point E in the fixed frame basis? Give your answer in terms of {i, j, k}.
E Provide kinematic equations for the position and velocity of point E on the long rope which is currently at the point of contact with the left side of the left-most pulley. Give your answer in the coordinates {i, j, k}. Define any other universal variables you choose to use.