Solution D1-30 (Figure D1.3 condition 0 S.M. Targ 1989)

Problem D1-30 (shown in Figure D1.3 in condition 0 S.M. Targ, 1989) is that a load of mass m, having received an initial speed v0 at point A, moves in a curved pipe ABC, which is located at vertical plane. The pipe sections are either both inclined, or one is horizontal and the other is inclined (Figures D1.0 - D1.9 and Table D1). At point AB, in addition to the force of gravity, the load is acted upon by a constant force Q (its direction is shown in the figures) and a resistance force of the medium R, depending on the speed v of the load (directed against the movement). In section AB, the friction of the load on the pipe can be neglected. At point B, the load moves to the section BC of the pipe without changing its speed, 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 is given in the table . The load can be considered as a material point. It is known that the distance AB is equal to l or the time t1 of movement of the load from point A to point B. It is necessary to determine the law of movement of the load on the section BC, that is, x = f(t), where x = BD.

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This product is a solution to problem D1-30 from the book by S.M. Targa, released in 1989. In this problem, we consider the movement of a mass m, which receives an initial speed v0 at point A and moves in a curved pipe ABC. The problem assumes the presence of sections of pipe with different angles of inclination, on which different forces act on the load.

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Solution to problem D1-30 from the book by S.M. Targa consists in determining the law of movement of the load on the section BC of the pipe, that is, x = f(t), where x = BD. To solve the problem, it is necessary to calculate the forces acting on the load at point BC and use the equation of motion of the material point.

In the section BC, a load of mass m is subject to a friction force directed opposite to the movement and equal to fN, where N is the normal force, and a variable force F, the projection of which Fx on the x axis is given in the table. The friction force is 0.2N, where f is the coefficient of friction of the load on the pipe. The normal force N is equal to the sum of the forces acting perpendicular to the surface of the pipe, that is, N = mg + Q - R, where m is the mass of the load, g is the acceleration of gravity, Q is the constant force acting on the load at point B, R is the resistance force environment depending on the speed of the load.

Considering that in the section BC the load moves at a constant speed, we can write the equation of motion of the load in projection onto the x-axis: Fx - fN = 0. Substituting the expression for N, we obtain the equation: Fx - f(mg + Q - R) = 0.

Next, using the table of Fx values ​​and the equation of motion, you can determine the value of the speed of the load on the aircraft section depending on time t. The solution to the problem is presented in a beautiful html design that preserves its structure, which makes it easier to study and understand the solution.

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Solution D1-30 is a physics problem that describes the movement of a load of mass m, which, having received an initial speed v0 at point A, moves in a curved pipe ABC located in a vertical plane. 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 of the load. At point B, the load moves to 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. 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, the task is to find the law of cargo movement in the aircraft section, i.e. x = f(t), where x = BD. The coefficient of friction between the load and the pipe is f = 0.2. The problem can be solved using Newton's laws and the equations of motion of a material point.

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