System Dynamics for Mechanical Engineers by Matthew A. Davies & Tony L. Schmitz

Author:Matthew A. Davies & Tony L. Schmitz
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Solution

First (step 1), we define the coordinates. In this case, we have the velocities, ω and v, as shown. The next step (step 2) is to draw free body diagrams of each inertia/mass in the system; these are displayed in Fig. 6.9.

Fig. 6.9Free body diagrams of the system elements from Fig. 6.8

Notice that there is an equal and opposite force from the cable, F, acting upward on the mass and downward on the pulley. Next, we apply Newton’s second law to each moving element. For the rotational inertia, we obtain Eq. (6.38) after substituting M b  = − bω.

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