Solution D6-56 (Figure D6.5 condition 6 S.M. Targ 1989)

The mechanical system described in solution D6-56 (condition 6 S.M. Targ, 1989) consists of loads 1 and 2, step pulley 3 with step radii R3 = 0.3 m, r3 = 0.1 m and radius of gyration ρ3 = 0.2 m, block 4 of radius R4 = 0.2 m and roller (or moving block) 5 (see figures D6.0 - D6.9 and table D6). Body 5 is a solid homogeneous cylinder, and the mass of block 4 is evenly distributed along its rim. The coefficient of friction of the loads on the plane is f = 0.1. The bodies of the system are connected to each other by threads thrown through blocks and wound on pulley 3 (or on a pulley and a roller); sections of threads are parallel to the corresponding planes. One of the bodies is connected to the spring with stiffness c. The force F = f(s) applied to the system depends on the displacement s of the point of its application and causes the system to move from a state of rest. The deformation of the spring at the moment the movement begins is zero. When moving, a constant moment M of resistance forces (from friction in the bearings) acts on pulley 3. The required value is indicated in the “Find” column of the table and can be expressed through the velocities of weights 1 (v1), 2 (v2) and the center of mass of body 5 (vC5), as well as the angular velocities of bodies 3 (ω3) and 4 (ω4). All rollers, including those wrapped in threads (for example, roller 5 in Figure 2), roll on planes without sliding. If the mass of load 2 is zero, then it does not need to be depicted in the figures; the remaining bodies must be depicted even if their mass is zero. To determine the value of the desired quantity at the moment of time when the displacement s becomes equal to s1 = 0.2 m, it is necessary to solve the corresponding equations of motion of the system.

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“Solution D6-56 (Figure D6.5 condition 6 S.M. Targ 1989)” is a digital product that is a unique solution to the mechanical system described in condition 6 S.M. Targ (1989). This mechanical system consists of weights 1 and 2, a stepped pulley 3, a block 4 and a roller (or moving block) 5. All bodies of the system are connected to each other by threads thrown through the blocks and wound on pulley 3 (or on the pulley and roller) , sections of threads are parallel to the corresponding planes. A spring with stiffness coefficient c is attached to one of the bodies. Under the influence of force F = f(s), which depends on the displacement s of the point of its application, the system begins to move from a state of rest.

The solution contains all the necessary figures and tables for understanding and solving the problem. The required value is determined at the moment of time when the displacement s becomes equal to s1 = 0.2 m. The desired value is indicated in the “Find” column of the table and can be expressed through the speeds of loads 1 (v1), 2 (v2) and the center of mass of the body 5 (vC5), as well as the angular velocities of bodies 3 (ω3) and 4 (ω4). The coefficient of friction of the loads on the plane is f = 0.1, and when moving on pulley 3 there is a constant moment M of resistance forces (from friction in the bearings). The system is solved on the basis of the equations of motion, and all rollers, including rollers wrapped in threads, roll on planes without slipping.

“Solution D6-56 (Figure D6.5 condition 6 S.M. Targ 1989)” is presented in a beautiful HTML design, which makes it easy and quick to find the information you need. This digital product can be useful to both students and professionals in the field of mechanics, and all materials included in the product are of high quality and tested for correct results. By purchasing this product, you get a unique opportunity to familiarize yourself with the solution to a mechanics problem in a convenient format that makes it easy to read and understand the conditions of the problem, as well as obtain the desired value at the moment in time when the displacement s becomes equal to s1 = 0.2 m.

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Solution D6-56 is a mechanical system consisting of two loads (load 1 and load 2), a stepped pulley 3 with step radii R3 = 0.3 m, r3 = 0.1 m and radius of gyration relative to the axis of rotation ρ3 = 0, 2 m, block 4 of radius R4 = 0.2 m and roller (or moving block) 5. Body 5 is considered a solid homogeneous cylinder, and the mass of block 4 is considered uniformly distributed along the rim. The coefficient of friction of the loads on the plane is f = 0.1.

The bodies of the system are connected to each other by threads thrown through blocks and wound on pulley 3 (or on a pulley and a roller). Sections of threads are parallel to the corresponding planes. A spring with stiffness coefficient c is attached to one of the bodies. Under the influence of force F = f(s), which depends on the displacement s of the point of its application, the system begins to move from a state of rest. The deformation of the spring at the moment the movement begins is zero.

When moving, pulley 3 is subject to a constant moment M of resistance forces (from friction in the bearings). It is necessary to determine the value of the desired quantity at the moment in time when the displacement s becomes equal to s1 = 0.2 m. The desired quantity is indicated in the “Find” column of the table, where it is indicated: v1, v2, vC5 - the speed of loads 1, 2 and the center of mass of the body 5, respectively, ω3 and ω4 are the angular velocities of bodies 3 and 4.

All rollers, including rollers wrapped in threads (such as roller 5 in Fig. 2), roll on planes without sliding. In all figures, do not depict load 2 if m2 = 0; the remaining bodies should also be depicted when their mass is zero.

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