Solution D6-26 (Figure D6.2 condition 6 S.M. Targ 1989)

Problem D6-26 (Figure D6.2 condition 6 S.M. Targ 1989) describes a mechanical system 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 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 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 of movement is zero. When moving, a constant moment M of resistance forces (from friction in the bearings) acts on pulley 3. 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 the following are 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. Load 2 is not depicted in all pictures if m2 = 0. The remaining bodies should be depicted even if their mass is zero.

This product is a solution to problem D6-26 from the textbook “Collection of problems for the general course of physics” by S.M. Targa published in 1989. The solution includes a description of a mechanical system consisting of weights, a pulley, a block and a roller connected by threads and a spring. To solve the problem, it is necessary to determine the required value at the moment in time when the displacement of the point of application of the force reaches a given value. The solution contains a detailed description of the system, formulas and solution methods, as well as a table with answers to all the required quantities. The design of the product is made in a beautiful html format, which allows you to conveniently read and study the material, visualize figures and tables.

This product is a solution to problem D6-26 from the textbook “Collection of problems for the general course of physics” by S.M. Targa, published in 1989. The solution describes a mechanical system consisting of weights, a pulley, a block and a roller connected by threads and a spring. To solve the problem, it is necessary to determine the required value at the moment in time when the displacement of the point of application of the force reaches a given value. The solution contains a detailed description of the system, formulas and solution methods, as well as a table with answers to all the required quantities. The design of the product is made in a beautiful html format, which allows you to conveniently read and study the material, visualize figures and tables. In addition, the description contains all the data necessary to understand the system and solve the problem, including the dimensions and characteristics of each element.

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Solution D6-26 (Figure D6.2 condition 6 S.M. Targ 1989) describes a mechanical system consisting of two loads (load 1 and load 2), a stepped pulley 3, a block 4 and a roller (or moving block) 5. Body 5 is a solid homogeneous cylinder; the mass of block 4 is considered to be 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). 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.

In this problem, it is required 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 - speeds of loads 1, 2 and center of mass of 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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