Solution D6-27 (Figure D6.2 condition 7 S.M. Targ 1989)

In problem D6-27 (condition 7, S.M. Targ, 1989), a mechanical system is considered, consisting of loads 1 and 2, a stepped pulley 3 with step radii R3 = 0.3 m, r3 = 0.1 m and radius of inertia relative to the axis of rotation ρ3 = 0.2 m, block 4 of radius R4 = 0.2 m and roller (or moving block) 5 (Fig. D6.0 - D6.9, Table D6). Body 5 is considered a solid homogeneous cylinder, and the mass of block 4 is evenly distributed along the rim. The coefficient of friction of the loads on the plane f is 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 of movement is zero. When moving, a constant moment M of resistance forces acts on pulley 3, caused by 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 and can be v1, v2, vC5 (velocities of loads 1, 2 and center of mass of the body 5 respectively), ω3 or ω4 (angular velocities of bodies 3 and 4). All rollers, including roller 5 in Fig. 2, roll on planes without slipping. If the mass of load 2 is zero, then it does not need to be depicted in the figures; the remaining bodies should be depicted even if their mass is zero.

Our digital goods store presents a unique solution to problem D6-27 (condition 7, S.M. Targ, 1989), which includes a detailed description of the mechanical system consisting of weights 1 and 2, step pulley 3, block 4 and roller 5, as well as images of all elements of the system in Figure D6.2. The solution indicates all the necessary parameters of the system, such as radii and coefficients of friction, and also describes the conditions for the movement of the system under the influence of a force that depends on the movement of the point of its application and a constant moment of resistance. In addition, the solution presents tables with the required quantities, which can be v1, v2, vC5, ω3 or ω4 depending on the specified displacement value s. The text is designed in a beautiful html style, which makes it easy to read and allows you to quickly find the information you need. Our solution is an indispensable assistant for students and teachers studying mechanics and physics, as well as for anyone interested in this topic.

Solution D6-27 (Figure D6.2 condition 7 S.M. Targ 1989) is a unique digital solution to the problem in mechanics, which includes a detailed description of the mechanical system consisting of weights 1 and 2, step pulley 3, block 4 and roller 5, as well as images of all elements of the system in Figure D6.2. The solution indicates all the necessary parameters of the system, such as radii and coefficients of friction, and also describes the conditions for the movement of the system under the influence of a force that depends on the movement of the point of its application and a constant moment of resistance. In addition, the solution presents tables with the required quantities, which can be v1, v2, vC5, ω3 or ω4 depending on the specified displacement value s. The text is designed in a beautiful html style, which makes it easy to read and allows you to quickly find the information you need. The solution is an indispensable assistant for students and teachers studying mechanics and physics, as well as for everyone who is interested in this topic.

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Solution D6-27 is a mechanical system consisting of weights 1 and 2, a stepped pulley 3, a block 4 and a roller (or moving block) 5. Body 5 is a solid homogeneous cylinder, and the mass of block 4 is evenly distributed along the rim. The coefficient of friction of the loads on the plane is 0.1. The bodies of the system are connected to each other by threads and 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. The figures and tables referred to in the assignment can be found in the book by S.M. Targa “Mechanics. Tasks. Part 1."

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