Solution D6-18 (Figure D6.1 condition 8 S.M. Targ 1989)

Solution to problem D6-18 (Condition 8 from the book by S.M. Targ, 1989)

The mechanical system consists of loads 1 and 2, step 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 a roller (or moving block) 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 (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 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 (for example, roller 5 in Fig. 2), roll on planes without sliding. All figures do not show load 2 if its mass is zero. The remaining bodies must be depicted.

Solving this problem requires the use of equations of motion for each body of the system and equations of connections between them. After this, it is necessary to differentiate and substitute the values ​​to find the desired value.

Be careful when solving the problem, pay attention to the units of measurement and do not forget about the laws of conservation of energy and angular momentum!

“Solution D6-18 (Figure D6.1 condition 8 S.M. Targ 1989)” is a digital product that is a solution to a problem from the book by S.M. Targa on mechanics. This problem describes a mechanical system consisting of several bodies connected by threads and subject to the influence of a force depending on the movement of the point of its application.

The solution to the problem is presented in html format with a beautiful design, which makes it convenient and easy to use. The product description indicates all the necessary parameters and conditions of the problem, and also describes in detail the method of solving it and the necessary steps to obtain the required value.

This digital product will be useful for students and teachers studying mechanics, as well as for anyone interested in physics and mathematics. By accessing this product, you can easily and quickly solve this problem, study its detailed solution and improve your knowledge in the field of mechanics.

Solution D6-18 is a digital product, which is a detailed solution to the problem from the book by S.M. Targa on mechanics. The problem describes a mechanical system consisting of weights, a stepped pulley, a block and a roller connected by threads, and subject to a force depending on the movement of its point of application.

The product description indicates all the necessary parameters and conditions of the problem, and also describes in detail the method of solving it and the necessary steps to obtain the required value. The solution is presented in html format with a beautiful design, which makes it convenient and easy to use.

To solve the problem, it is necessary to use the equations of motion for each body of the system and the equations of connections between them. After this, it is necessary to differentiate and substitute the values ​​to find the desired value. The problem also needs to take into account the laws of conservation of energy and angular momentum.

This digital product will be useful for students and teachers studying mechanics, as well as for anyone interested in physics and mathematics. By accessing this product, you can easily and quickly solve this problem, study its detailed solution and improve your knowledge in the field of mechanics.

Solution D6-18 (Figure D6.1 condition 8 S.M. Targ 1989) is a description of the solution to the problem in mechanics from the book by S.M. Targa. This problem considers a mechanical system consisting of several bodies connected by threads and subject to a force that depends on the movement of the point of its application.

The mechanical system consists of weights 1 and 2, a stepped pulley 3, a block 4 and a roller (or moving block) 5. The body 5 is considered a solid homogeneous cylinder, and the mass of the 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 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 (for example, roller 5 in Fig. 2), roll on planes without sliding. All figures do not show load 2 if its mass is zero. The remaining bodies must be depicted.

Solving the problem requires the use of equations of motion for each body of the system and equations of connections between them. After this, it is necessary to differentiate and substitute the values ​​to find the desired value.

The solution is presented in html format with a beautiful design, which makes it convenient and easy to use. The product description indicates all the necessary parameters and conditions of the problem, and also describes in detail the method of solving it and the necessary steps to obtain the required value.

This digital product will be useful for students and teachers studying mechanics, as well as for anyone interested in physics and mathematics. Having access to this product, you can easily and quickly solve a complex mechanical problem and obtain the desired value. It will help you better understand the physical laws associated with the movement of bodies and the connections between them, and teach you how to apply them in practice.

However, I cannot provide you with this digital product as I do not have access to commercial products. I can only help you with specific questions in physics and mechanics, or talk about the theoretical aspects of these sciences. If you have any questions or difficulties, feel free to ask and I will try to help you.

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Solution D6-18 is a mechanical system consisting of two loads (1 and 2), a stepped pulley 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, block 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 along the rim. 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 pulley 3 (or on a pulley and roller), 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 of movement 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. 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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