Solution D6-15 (Figure D6.1 condition 5 S.M. Targ 1989)

The mechanical system described in solution D6-15 (Figure D6.1, condition 5, S.M. Targ, 1989) consists of weights 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, 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 is considered a solid homogeneous cylinder, and the mass of block 4 is distributed evenly 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. One of the springs with stiffness coefficient c is attached to one of the bodies. The system moves from a state of rest under the action of a force F = f(s), depending on the displacement s of the point of its application, while the deformation of the spring at the moment of the start 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 and is designated as v1, v2, vC5 (velocities of loads 1, 2 and center of mass of the body 5 respectively), as well as ω3 and ω4 (angular velocities of bodies 3 and 4). All rollers, including those wrapped in threads (such as roller 5 in Figure 2), roll on planes without slipping. Load 2 is not depicted in the figures if its mass is zero, but all other bodies are depicted in any case.

Welcome to our digital goods store! We present to you a digital product - "Solution D6-15 (Figure D6.1 condition 5 S.M. Targ 1989)". This product is a solution to a mechanical system that consists of several bodies connected to each other by threads and springs. The solution is provided in the form of a table, which indicates the velocities of the loads and the angular velocities of the bodies of the system at the moment of time when the movement of the point of application of the force becomes equal to 0.2 m. The table also indicates all the necessary parameters of the system, such as the radii of the pulley steps, the coefficient of friction of the loads on the plane and constant moment of resistance forces. Solution D6-15 was developed by S.M. Targ in 1989 and still remains relevant and useful for specialists in the field of mechanics. We hope that our digital product will help you solve your problems and be useful for your work!

This product is a digital solution of a mechanical system consisting of weights, a stepped pulley, a block and a roller, connected by threads and springs. The solution was developed by S.M. Targ in 1989 and presented in the form of a table in which all the necessary parameters of the system are indicated, including the radii of the pulley steps, the coefficient of friction of the loads on the plane and the constant moment of resistance forces. The table also shows the velocities of the loads and the angular velocities of the bodies of the system at the moment of time when the displacement of the point of application of the force becomes equal to 0.2 m. The solution can be useful for specialists in the field of mechanics when solving similar problems. The product is presented in the form of an electronic document and will be available for download after payment.

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Solution D6-15 (Figure D6.1 condition 5 S.M. Targ 1989) is a problem from the textbook by S.M. Targa "Physics Problem Book" 1989 edition. It belongs to the section of mechanics and kinematics.

The problem statement considers the motion of a body thrown at an angle to the horizontal. It is required to solve the problem and determine the maximum lifting height of the body and the maximum flight range.

The solution to the problem is to apply the laws of mechanics and kinematics, in particular, the equations of body motion in the vertical and horizontal planes. It is also necessary to take into account the influence of gravity and air resistance on the movement of the body.

The final answer depends on the initial conditions of the problem, including the initial speed and angle of the throw. Solution D6-15 can be used to study the kinematic laws of motion of bodies in space and the practical applications of this theory in physics and engineering.

Solution D6-15 is a mechanics problem that describes the movement of a mechanical system consisting of loads 1 and 2, a stepped pulley 3, a block 4, a roller 5 and a spring, under the action of a force F = f(s), depending on the displacement s of its point applications. 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.

In the problem, 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 - speeds of loads 1, 2 and center masses of body 5, respectively, ω3 and ω4 are the angular velocities of bodies 3 and 4.

To solve the problem, it is necessary to use the laws of mechanics, including the law of conservation of energy and the law of conservation of momentum. It is also necessary to take into account the friction of the loads on the plane and the resistance force acting on pulley 3.

When solving a problem, you must perform the following steps:

1. Find the acceleration of loads 1 and 2 and the center of mass of body 5.
2. Find the tension forces of the threads acting on each of the bodies of the system.
3. Find the moment of inertia of pulley 3 relative to the axis of rotation.
4. Find the moment of friction force acting on pulley 3.
5. Find the moment of force acting on block 4.
6. Find the angular acceleration of pulley 3 and block 4.
7. Find the linear speeds of loads 1 and 2 and the center of mass of body 5.
8. Find the angular speeds of pulley 3 and block 4.
9. Find the required value at the moment of time when the displacement s becomes equal to s1 = 0.2 m.

All rollers, including rollers wrapped in threads, roll on planes without slipping. 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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