Solution D6-24 (Figure D6.2 condition 4 S.M. Targ 1989)

In problem D6-24 (from condition 4, S.M. Targ, 1989), a mechanical system is considered, consisting of two loads (1 and 2), a stepped pulley 3 with step radii: R3 = 0.3 m, r3 = 0.1 m and radius of gyration ρ3 = 0.2 m relative to the axis of rotation, 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 over 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. The force F = f(s) applied to the system depends on the displacement s of the point of its application and leads to the beginning of the system’s motion 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 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, 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 (for example, roller 5 in Fig. 2), roll on planes without sliding. If m2 = 0, load 2 is not depicted in the figures, but all other bodies must be depicted, even if their mass is zero.

Our digital goods store presents a solution to problem D6-24 (from condition 4, S.M. Targ, 1989). This digital product contains a detailed description of a mechanical system consisting of two weights, a step pulley, a block, a roller, and a spring with a spring constant of c. The solution to this problem shows the values ​​of the required quantities at the moment of time when the displacement s becomes equal to s1 = 0.2 m. All data is presented in a convenient table, which indicates the speed of the loads, the center of mass of the body and the angular velocities of bodies 3 and 4. In addition, , the solution contains Figure D6.2, which clearly shows the mechanical system and connections between bodies. All material is presented in a beautiful html format, which makes it easy to read and understand the solution to the problem. By purchasing this digital product, you will receive useful material for studying mechanics and solving similar problems.

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Solution D6-24 is a mechanical system consisting of two weights (1 and 2), a stepped pulley (3), a block (4) and a roller (5). The pulley has step radii R3 = 0.3 m, r3 = 0.1 m and radius of gyration ρ3 = 0.2 m. The block has a radius R4 = 0.2 m and a mass uniformly distributed along the rim. Body 5 is considered a solid homogeneous cylinder. The coefficient of friction of the loads on the plane is f = 0.1.

All bodies of the system are connected to each other by threads thrown through blocks and wound on a 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 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 and can be v1, v2, vC5 (velocities of loads 1, 2 and center of mass of the body 5 respectively) or ω3 and ω4 (angular velocities of bodies 3 and 4). All rollers, including rollers wrapped in threads, roll on planes without slipping. If the mass of load 2 is zero, then it is not depicted in the figure, but the remaining bodies must be depicted.

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