# 4-56 - Problem 4.56 Giancoli I have gotten several...

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Problem 4.56, Giancoli I have gotten several questions about problem 4.56 in Giancoli, which is on the homework, so I am writing this document to help you out a little bit. Normally, the approach we would take with a force problem would be: (1) Draw a free body diagram, (2) write F = ma equations for each FBD, (3) substitute in any known or related quantities, (4) solve for any unknown quantities. In step 3, you would do things like replace the force of friction with μN . In Lab 3, for example, we used the fact that the cart and the hanging mass had the same acceleration because they were tied together. Here, there is clearly a relationship between the various accelerations, but it is not easy to immediately identify like in Lab 3. We will use a more formal approach to ﬁnd the “kinematic constraint” on this problem. Figure 1: Problem 4.56, Giancoli, with Established Coordinate Systems Kinematic Constraint. Looking at ﬁgure 1, we see the problem presented in Giancoli, but I have included some coordinates to measure the various positions. The vector y c , drawn in black, represents the position of block C as measured from the center of the top pulley. We measure the other two blocks, as shown in blue, from that same point, and we call these y a and y b . Since the bottom pulley also moves, we measure its position (measured from the top pulley as well) and call

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4-56 - Problem 4.56 Giancoli I have gotten several...

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