Solution D5-55 (Figure D5.5 condition 5 S.M. Targ 1989)

The solution to problem D5-55 (Figure D5.5, condition 5 from the book by S.M. Targ 1989) is to determine the dependence of the angular velocity of the platform ω on time t. In this problem, there is a homogeneous horizontal platform, which can be circular with radius R or rectangular with sides R and 2R, where R = 1.2 m, with mass m1 = 24 kg. The platform rotates with an initial angular velocity ω0 = 10 s-1 around the vertical axis z, located at a distance OC = b from the center of mass C of the platform (Fig. D5.0 - D5.9, Table D5). Dimensions for all rectangular platforms are shown in Fig. D5.0a (top view).

At the moment of time t0 = 0, a load D with a mass m2 = 8 kg begins to move along the platform chute, under the influence of internal forces, according to the law s = AD = F(t), where s is expressed in meters, t - in seconds. At the same time, a pair of forces with a moment M (given in newton meters; at M 0 (when s

To solve the problem, it is necessary to draw the z axis at a given distance OC = b from the center C and determine the dependence ω = f(t), neglecting the shaft mass.

This digital product is a solution to problem D5-55 from the book by S.M. Targa 1989. The solution includes a detailed description of the problem, graphic images and tables with data.

A homogeneous horizontal platform (circular with radius R or rectangular with sides R and 2R) with mass m1 = 24 kg rotates with angular velocity ω0 = 10 s-1 around the vertical axis z, spaced from the center of mass C of the platform at a distance OC = b. At the moment of time t0 = 0, a load D with a mass of m2 = 8 kg begins to move along the platform chute under the action of internal forces specified by the law of motion s = AD = F(t), where s is expressed in meters, t in seconds. At the same time, a pair of forces with a moment M (given in newton meters) begins to act on the platform.

The solution contains formulas and calculations necessary to determine the dependence of the platform angular velocity ω on time t for given parameters. All data is presented in a readable format with a beautiful html design, which allows you to quickly and efficiently study the material.

This product will be useful for students, teachers and anyone interested in mechanics and physics. It can be used both for independent work and for preparing for exams and tests.

This product is a solution to problem D5-55 from the book by S.M. Targa 1989. The task is to determine the dependence of the angular velocity of the platform ω on time t. To do this, it is necessary to draw the z axis at a given distance OC = b from the center C and determine the dependence ω = f(t), neglecting the shaft mass.

The problem involves a homogeneous horizontal platform, which can be circular with radius R or rectangular with sides R and 2R, where R = 1.2 m, with mass m1 = 24 kg. The platform rotates with an initial angular velocity ω0 = 10 s-1 around the vertical axis z, located at a distance OC = b from the center of mass C of the platform. At the moment of time t0 = 0, a load D with a mass m2 = 8 kg begins to move along the platform chute, under the influence of internal forces, according to the law s = AD = F(t), where s is expressed in meters, t - in seconds. At the same time, a pair of forces with a moment M (given in newton meters) begins to act on the platform.

The solution contains formulas and calculations necessary to determine the dependence of the platform angular velocity ω on time t for given parameters. All data is presented in a readable format with a beautiful html design, which allows you to quickly and efficiently study the material.

This product will be useful for students, teachers and anyone interested in mechanics and physics. It can be used both for independent work and for preparing for exams and tests.

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Solution D5-55 is a device consisting of a homogeneous horizontal platform, which can be circular with radius R or rectangular with sides R and 2R, where R = 1.2 m, and has a mass m1 = 24 kg. The platform rotates with an angular velocity ω0 = 10 s-1 around a vertical axis z, located at a distance OC = b from the center of mass C of the platform.

At the moment of time t0 = 0, a load D of mass m2 = 8 kg begins to act on the platform, which moves along the platform groove under the action of internal forces. The movement of the load is described by the law s = AD = F(t), where s is expressed in meters, t in seconds.

At the same time, a pair of forces with a moment M, which is specified in newtonometers, begins to act on the platforms. At M0 (when s<0) the platform stops. The platform is also affected by the force of gravity, which is directed vertically downward and equal to mg, where g is the acceleration of gravity.

For all rectangular platforms, the dimensions are shown in Figure D5.0a (top view). Table D5 shows the values ​​of the moment of inertia of the platform relative to the z-axis and the distance OC from the center of mass to the axis of rotation for various platform configurations.

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