Solution D1-23 (Figure D1.2 condition 3 S.M. Targ 1989)

Solution to problem D1-23, presented in Figure D1.2, condition 3 from the book by S.M. Targa 1989, consists in considering the movement of a load of mass D and mass m, which begins to move with an initial speed v0 at point A. The movement of the load occurs in a curved pipe ABC, which is located in a vertical plane. Pipe sections can be inclined or horizontal (see Figures D1.0 - D1.9 and Table D1).

In section AB, in addition to the force of gravity, the load is acted upon by a constant force Q, the direction of which is indicated in the figures, and a resistance force of the medium R, which depends on the speed v of the load and is directed against the movement. In this case, we neglect the friction between the load and the pipe in section AB.

At point B, the load, without changing its speed, moves to the section BC of the pipe, where, in addition to the force of gravity, it is acted upon by the friction force (friction coefficient of the load on the pipe f = 0.2) and the variable force F, the projection of which Fx on the x axis given in the table.

Considering the load to be a material point and knowing the distance AB = l or the time t1 of movement of the load from point A to point B, it is necessary to find the law of movement of the load on the section BC, i.e. x = f(t), where x = BD.

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This digital product includes the solution to problem D1-23, presented in Figure D1.2, condition 3. The solution is presented in a beautiful html format that will allow you to easily navigate the text and quickly find the necessary information.

Using this solution, you can calculate the law of motion of a load of mass D and mass m, which moves in a curved pipe ABC located in a vertical plane. You will learn what forces act on the load on each section of the pipe, how they affect its movement and how to calculate the law of movement of the load on the aircraft section.

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The proposed digital product is a complete and high-quality solution to problem D1-23 from the book by S.M. Targa 1989. The solution is presented in the form of a beautiful HTML document that will make it easy to navigate the text and quickly find the necessary information.

The problem is to consider the movement of a load of mass D and mass m, which begins to move with an initial speed v0 at point A. The movement of the load occurs in a curved pipe ABC, which is located in a vertical plane. Pipe sections can be inclined or horizontal.

In section AB, in addition to the force of gravity, the load is acted upon by a constant force Q and a resistance force of the medium R, which depends on the speed v of the load and is directed against the movement. In this case, the friction between the load and the pipe in section AB is neglected.

At point B, the load, without changing its speed, moves to the section BC of the pipe, where, in addition to the force of gravity, it is affected by the friction force (friction coefficient of the load on the pipe f = 0.2) and the variable force F, the projection of which Fx on the x axis is given in table.

Considering the load as a material point and knowing the distance AB = l or the time t1 of movement of the load from point A to point B, it is necessary to find the law of movement of the load in the section BC, i.e. x = f(t), where x = BD.

By purchasing the offered digital product, you will be able to calculate the law of movement of the load on the aircraft section, find out what forces act on the load on each section of the pipe and how they affect its movement. The resulting solution will help you successfully complete the task and achieve your goals.


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Solution D1-23 depicts a mass m moving in a vertical plane in a curved pipe ABC. The load receives an initial speed v0 at point A and moves along the section AB of the pipe, on which the force of gravity, the constant force Q and the resistance force of the medium R, depending on the speed of the load, act. At point B, the load passes to the section BC of the pipe, where, in addition to the force of gravity, it is acted upon by the friction force and the variable force F, the projection of which Fx on the x axis is given in the table. The coefficient of friction between the load and the pipe is f = 0.2.

The task is to find the law of cargo movement on the aircraft section, i.e. find the function x = f(t), where x is the distance between point B and the current position of the load BD, and t is the time of movement of the load on the section BC. To do this, it is necessary to use known parameters, such as the mass of the load m, the initial speed v0, the constant force Q, the resistance force of the medium R, the coefficient of friction f, the variable force Fx, the distance l between points A and B or the time t1 of movement of the load from point A to points B.

The problem can be solved by applying Newton's laws for the motion of a material point in a gravitational field, as well as the equation of motion taking into account the friction force and the variable force Fx.


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