Problem 2: (37 points) The system shown in the figure consists of two blocks (masses: M1, M2), a cylinder (radius R3, ma

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Problem 2 37 Points The System Shown In The Figure Consists Of Two Blocks Masses M1 M2 A Cylinder Radius R3 Ma 1 (132.32 KiB) Viewed 74 times

Problem 2: (37 points) The system shown in the figure consists of two blocks (masses: M1, M2), a cylinder (radius R3, mass m3) a spool (inner radius r4, outer radius R4, mass m4, moment of inertia with respect to its center of mass J.), two massless pulleys and two massless ropes. Rope 1 connects the blocks, which are sliding on inclined planes. Rope 2 is wrapped around the inner radius of the spool at one side, passing over the cylinder and fixed to the left side of the upper block 2. A massless rod connects the block 1 to a massless pulley. The whole system shall be considered frictionless. Assume there is no slipping between the ropes and the cylinder, spool and pulleys. All bodies are homogeneous. 9 43 R3 12 112 m3 44 mi 14 B 04 RA (a) Draw free body diagrams for the blocks, the cylinder and the spool, including all reaction forces. (b) State Newton's Law for the blocks. Make use of the given directions for the accelerations i and 22. The equations for the yı- and y2-component are not required. (c) State Newton's Law for the spool. Make use of the given direction for the acceleration 24 of its center of mass. The equation for the ja-component is not required. (d) State Euler's Law for the spool and the cylinder. Make use of the given directions for the angular accelerations P3 and PA. Hint: The moment of inertia for a homogeneous cylinder (mass m, radius r) with respect to its central axis is Jc = žmr². The moment of inertia for the spool is Jy and can be assumed given. (e) Determine the kinematic relationship between C2 and 23 as well as ïi and P3. (f) Determine the kinematic relationship between 22, 24, and 04. Hint for the spool: Consider superimposition of translation and rotation. (9) Assuming that the bearing of the cylinder breaks so that only the spool is moving, determine all rope forces in terms of mi, m2, a, B and g. Kostenlos heruntergeladen von S Studydrive