Solution D6-76 (Figure D6.7 condition 6 S.M. Targ 1989)

The problem with solution D6-76 shows a mechanical system consisting of loads 1 and 2, step pulley 3, block 4 and roller 5. Pulley 3 has step radii R3 = 0.3 m and r3 = 0.1 m, as well as the radius inertia ρ3 = 0.2 m. Block 4 has a radius R4 = 0.2 m, and roller 5 is considered a solid homogeneous cylinder. The mass of block 4 is evenly distributed over 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 over blocks and wound on pulley 3 and roller 5. 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. 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 when the displacement s becomes equal to s1 = 0.2 m. The desired quantity is indicated in the “Find” column of the table and is designated as v1, v2, vC5, ω3 and ω4 - the speed of loads 1, 2 and the center of mass of the body 5 , as well as the angular velocities of bodies 3 and 4, respectively. All rollers, including rollers wrapped in threads, roll on planes without slipping. All figures do not show load 2 if its mass is zero. The solution to this problem was proposed by S.M. Targ in 1989.

Here is a digital solution to problem D6-76, which was proposed by S.M. Targ in 1989. The solution includes Figure D6.7 and condition 6 of the problem. A mechanical system consisting of weights, a stepped pulley, a block and a roller is shown in the figure. The problem statement describes the characteristics of each body in the system, including their mass and coefficient of friction. The force acting on the system and the constant moment of resistance forces are also specified. In solving this problem, it is necessary to determine the value of the required quantity at the moment of time when the displacement of the point of application of the force becomes equal to 0.2 m. The table shows the required quantities, such as the velocities of the loads and the angular velocities of the bodies of the system. This digital product is designed for students and teachers who are learning mechanics and want to practice solving problems.

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The D6-76 solution is a mechanical system consisting of two weights, a stepped pulley, a block and a roller. The system is connected by threads thrown through blocks and wound on a pulley and roller. One of the bodies of the system has a spring attached to it with a stiffness coefficient c. The motion of the system is caused by the action of force F, which depends on the movement of the point of its application. When moving, pulley 3 is subject to a constant moment M of resistance forces caused by friction in the bearings.

The required value is indicated in the “Find” column of the table and can be one of the following: v1, v2, vC5, ω3, ω4 - speed of load 1, speed of load 2, speed of the center of mass of the body 5, angular speed of the stepped pulley 3 and angular speed of the block 4 respectively.

All rollers, including rollers wrapped in threads, roll on planes without slipping. In all figures, do not depict load 2 if its mass is zero; the remaining bodies should also be depicted when their mass is zero. The coefficient of friction of the loads on the plane is f = 0.1. Body 5 is considered to be a solid homogeneous cylinder, and the mass of block 4 is considered to be evenly distributed along the rim.

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