Solution D6-70 (Figure D6.7 condition 0 S.M. Targ 1989)

In problem D6-70 (see Figure D6.7, condition 0, 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 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 (see figures D6.0 - D6.9 and table D6 ). Body 5 should be considered a solid homogeneous cylinder, and the mass of block 4 should be 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. 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. 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. If m2 = 0, load 2 is not depicted in all figures; the remaining bodies should be depicted, even if their mass is zero.

The digital goods store presents a solution to problem D6-70, in accordance with the condition shown in Figure D6.7 from the book by S.M. Targa 1989. This digital product is a document designed in a beautiful HTML format that retains the structure of the table and figures from the original book. The solution contains all the necessary calculations and formulas necessary to solve this mechanical problem. The solution includes a detailed description of the mechanical system, its properties and parameters. In addition, the solution contains a table with the necessary data and the answer to the problem in the "Find" column, indicating the values ​​of the speed and angular velocity of the system at a given time. This digital product is a useful resource for anyone studying mechanics or doing research in the field.

Solution D6-70 (Figure D6.7 condition 0 S.M. Targ 1989) is a digital product in the form of a document in a beautiful HTML format that preserves the structure of the table and figures from the original book. The solution contains a detailed description of the mechanical system, its properties and parameters. The solution contains all the necessary calculations and formulas necessary to solve this mechanical problem.

The mechanical system consists of weights 1 and 2, a stepped pulley 3, a block 4 and a roller 5. 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 and roller 5; 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, 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 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, roll on planes without sliding. If m2 = 0, load 2 is not depicted in all figures; the remaining bodies should be depicted, even if their mass is zero.

This digital product is a useful resource for anyone studying mechanics or doing research in the field.

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The D6-70 solution is a mechanical system consisting of two weights (weight 1 and weight 2), a stepped pulley 3, a block 4 and a roller 5. The weights are connected by threads thrown over the blocks and wound on the pulley and roller. A spring with stiffness coefficient c is attached to one of the weights. The coefficient of friction of the loads on the plane is f=0.1. Under the influence of force F=f(s), depending 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, roll on planes without sliding.

Body 5 is considered a solid homogeneous cylinder, and the mass of block 4 is evenly distributed along the rim. Sections of threads are parallel to the corresponding planes. The radii of the pulley 3 steps are equal to R3=0.3 m and r3=0.1 m, and the radius of inertia relative to the axis of rotation is equal to ρ3=0.2 m. The radius of block 4 is R4=0.2 m.

This mechanical system is described by Figure D6.7 in the book by S.M. Targa "Problem book on general physics". Solving the problem involves using knowledge of mechanics and mathematical analysis.

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