Solution D6-51 (Figure D6.5 condition 1 S.M. Targ 1989)

Mechanical system shown in Figure D6.5 condition 1 S.M. Targ 1989 and designated as solution D6-51, consists of two weights (weight 1 and weight 2), a stepped pulley 3 and a block 4 of radius R4 = 0.2 m, as well as a roller (or moving block) 5. The radii of the pulley steps 3 are R3 = 0.3 m and r3 = 0.1 m, and the radius of gyration relative to the axis of rotation is ρ3 = 0.2 m. The mass of block 4 should be distributed evenly over the entire rim. Body 5 is a solid homogeneous cylinder.

The bodies of the system are connected to each other by threads thrown over blocks and wound on pulley 3 (or on a pulley and roller), and sections of the 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, while the deformation of the spring at the moment of the start of movement is zero. The coefficient of friction of the loads on the plane is f = 0.1. During movement, 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 and can be one of the following: v1, v2, vC5 - speeds of loads 1, 2 and the center of mass of body 5, respectively, and 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 its mass is zero; the rest of the bodies should be depicted in any case.

Solution D6-51

Solution D6-51 is a digital product that represents a solution to a mechanics problem from S.M.’s textbook. Targa, published in 1989. The solution describes a mechanical system consisting of weights, a stepped pulley, a block and a roller, connected by threads and a spring. The solution involves determining the required value at the moment in time when the displacement of the point of application of the force reaches the value s1 = 0.2 m.

The D6-51 solution is ideal for students and teachers studying mechanics, as well as for anyone interested in physics and mathematics. The solution is presented in the form of a beautifully designed HTML document containing a detailed description of the mechanical system and a step-by-step solution to the problem. All information is presented clearly and easily understandable.

By purchasing Solution D6-51, you receive a high-quality digital product that will help you better understand mechanics and solve problems successfully. Beautiful design and convenient format make it easy and quick to find the necessary information and use it in study or practice.

Solution D6-51 (Figure D6.5 condition 1 S.M. Targ 1989) is a digital product that is a solution to a mechanics problem from the textbook by S.M. Targa, published in 1989. The solution describes a mechanical system consisting of weights, a stepped pulley, a block and a roller, connected by threads and a spring.

The solution includes determining the desired value at the moment of time when the movement of the point of application of the force reaches the value s1 = 0.2 m. The desired value can be one of the following: the speed of loads 1, 2 and the center of mass of body 5, as well as the angular velocities of bodies 3 and 4.

The D6-51 solution is ideal for students and teachers studying mechanics, as well as for anyone interested in physics and mathematics. The solution is presented in the form of a beautifully designed HTML document containing a detailed description of the mechanical system and a step-by-step solution to the problem.

All information is presented clearly and easily understandable. By purchasing Solution D6-51, you receive a high-quality digital product that will help you better understand mechanics and solve problems successfully. Beautiful design and convenient format make it easy and quick to find the necessary information and use it in study or practice.

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Solution D6-51 is a mechanical system that consists 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 relative to the axis of rotation ρ3 = 0 .2 m, a block (4) of radius R4 = 0.2 m and a roller (or moving block) (5). The body (5) is considered to be a solid homogeneous cylinder, and the mass of the block (4) is considered to be 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 a pulley (3) (or on a pulley 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, 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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Peculiarities:

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