Solution D1-32 (Figure D1.3 condition 2 S.M. Targ 1989)

The solution to problem D1-32 (Figure D1.3 condition 2 S.M. Targ 1989) consists in considering the movement of a load of mass m, which received an initial speed v0 at point A and 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 v of the load and is directed against the movement. Pipe sections can be inclined or one of them can be horizontal (Fig. D1.0 - D1.9, Table D1).

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 that the friction of the load on the pipe in section AB can be neglected, it is necessary to find the law of movement of the load in section BC, i.e. x = f(t), where x = BD and the distance AB = l or time t1 of movement of the load from the point is known A to point B.

To solve the problem it is necessary to apply the laws of motion and Newton's equations. Since the load is considered a material point, its movement can be described using the equation of motion of a point:

x = x0 + v0t + (at^2)/2,

where x0 is the initial position of the point, v0 is the initial velocity, a is the acceleration of the point.

In the section AB, where the constant force Q and the resistance force of the medium R act, the acceleration of the point can be represented as:

a = (Q - mg - R)/m,

where g is the acceleration of gravity.

In the section BC, where the friction force and the variable force F act, the acceleration of the point will be equal to:

a = (F - mg - fN)/m,

where N is the normal force, which is equal to the force of gravity on the BC section.

To find the normal force N, you can use the equilibrium condition along the y axis:

N - mg - Fy = 0,

where Fy is the projection of force F on the y-axis.

Using the obtained equations, it is possible to determine the law of cargo movement in the aircraft section, i.e. x = f(t), where x = BD.

We present to your attention a digital product - Solution D1-32 (Figure D1.3 condition 2 S.M. Targ 1989) - a complete solution to the problem with a detailed description and solution steps. This product is ideal for students and teachers who study physics and mechanics.

We provide you with a beautifully designed html document that is easy to read and understand. The document contains graphic images, tables and other elements that will help you quickly understand the solution to the problem.

By purchasing this product, you receive a quality product that will help you quickly and easily understand the topic and successfully complete the task.

We present to your attention the product “Solution D1-32 (Figure D1.3 condition 2 S.M. Targ 1989)”, which includes a complete solution to the problem with a detailed description and solution steps.

The problem is to consider the movement of a load of mass m, which received an initial speed v0 at point A and 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 v of the load and is directed against the movement. Pipe sections can be inclined or one of them can be horizontal (Fig. D1.0 - D1.9, Table D1).

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.

To solve the problem it is necessary to apply the laws of motion and Newton's equations. Since the load is considered a material point, its movement can be described using the equation of motion of a point:

x = x0 + v0t + (at^2)/2,

where x0 is the initial position of the point, v0 is the initial velocity, a is the acceleration of the point.

In the section AB, where the constant force Q and the resistance force of the medium R act, the acceleration of the point can be represented as:

a = (Q - mg - R)/m,

where g is the acceleration of gravity.

In the section BC, where the friction force and the variable force F act, the acceleration of the point will be equal to:

a = (F - mg - fN)/m,

where N is the normal force, which is equal to the force of gravity on the BC section.

To find the normal force N, you can use the equilibrium condition along the y axis:

N - mg - Fy = 0,

where Fy is the projection of force F on the y-axis.

Using the obtained equations, it is possible to determine the law of cargo movement in the aircraft section, i.e. x = f(t), where x = BD.

The product presented includes a beautifully designed html document that is easy to read and understand. The document contains graphic images, tables and other elements that will help you quickly understand the solution to the problem. This product is ideal for students and teachers who study physics and mechanics. By purchasing this product, you receive a quality product that will help you quickly and easily understand the topic and successfully complete the task.

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Solution D1-32 is a mechanics problem that describes the movement of a load of mass m, which receives an initial speed v0 at point A and moves along a curved pipe ABC located in a vertical plane. In section AB, 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 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 Fx, the projection of which is given in the table and depends on time. The coefficient of friction between the load and the pipe is f=0.2.

It is necessary to find the law of cargo movement on the aircraft section, that is, determine the dependence of the coordinate x=BD on time t. To do this, you need to know the distance between points A and B, l, or the time of movement of the load from point A to point B, t1.

To solve the problem, it is necessary to apply the laws of mechanics, taking into account the forces acting on the load and the conditions of movement in the pipe.

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