Solution K3-28 (Figure K3.2 condition 8 S.M. Targ 1988)

In problem K3-28 from the conditions of S.M. Targa, it is necessary to determine the absolute speed and acceleration of point M at time t1 = 1 s. To do this, we consider the rotation of a rectangular plate (Figures K3.0-K3.5) or a round plate with radius R = 60 cm (Figures K3.6-K3.9) around a fixed axis with an angular velocity ω specified in the table. K3 (with a minus sign, the direction of ω is opposite to that shown in the figure).

In Figures K3.0-K3.3 and K3.8, K3.9 the axis of rotation is perpendicular to the plane of the plate and passes through point O (the plate rotates in its plane), and in Figures K3.4-K3.7 the axis of rotation OO1 lies at plane of the plate (the plate rotates in space). Point M moves along the plate along straight line BD (Figures K3.0-K3.5) or along a circle of radius R, i.e., along the rim of the plate (Figures K3.6-K3.9), and its motion is described by the law s = AM = f(t) (where s is in centimeters, t is in seconds), given in table. K3 separately for figures K3.0-K3.5 and K3.6-K3.9. In this case, in Figures K3.6-K3.9 s = AM and is measured along the arc of a circle, and dimensions b and l are also given.

It is important to note that in all figures point M is shown in a position at which s = AM > 0 (with s

To solve the problem, it is necessary to use formulas for finding the absolute speed and acceleration of point M on the plate, as well as the vector equation of motion. The calculation results for time t1 = 1 s will allow us to determine the required values.

Solution K3-28 (Figure K3.2 condition 8 S.M. Targ 1988)

The solution to K3-28 is a problem from the conditions of S.M. Targa, which consists in determining the absolute speed and acceleration of point M on the plate at time t1 = 1 s.

To solve the problem, it is necessary to use formulas for finding the absolute speed and acceleration of point M on the plate, as well as the vector equation of motion. The calculation results for time t1 = 1 s will allow us to determine the required values.

The problem describes the rotation of a rectangular plate or a circular plate of radius R = 60 cm around a fixed axis with an angular velocity ω given in Table. K3 (with a minus sign, the direction of ω is opposite to that shown in the figure). The movement of point M occurs along a straight line BD or along a circle of radius R, i.e., along the rim of the plate, and its movement is described by the law s = AM = f(t) (where s is in centimeters, t is in seconds), given in table . K3 separately for rectangular plate and round plate.

Solution K3-28 is an excellent example of a kinematics problem that can be used for educational purposes, as well as for calculations in scientific and engineering projects.

> 0 point M is located to the right of point A).

To solve problem K3-28, it is necessary to determine the absolute speed and acceleration of point M on the plate at time t1 = 1 s. To do this, you should use formulas for finding the absolute speed and acceleration of point M on the plate, as well as the vector equation of motion.

When solving the problem, it is necessary to take into account that the plate rotates around a fixed axis with a constant angular velocity, and point M moves along a straight line or along a circle of radius R, i.e. its movement is described by the law s = AM = f(t). The values ​​of s and t for given times t1 can be found in table K3.

So, to solve the problem you need to perform the following steps:

1. Determine the type of plate (rectangular or round) and its dimensions (radius R for a round plate, b and l for a rectangular one).
2. Find the angular velocity of the plate according to table K3.
3. Find the position of point M on the plate at time t1 according to table K3.
4. Determine the velocity vector of point M at time t1, using the formula for the absolute velocity of a point on a rotating body.
5. Determine the acceleration vector of point M at time t1, using the formula for the absolute acceleration of a point on a rotating body.
6. Interpret the results obtained and give an answer to the task.

The solution to problem K3-28 can be used to study the kinematics of rotational motion and calculate the speed and acceleration of points on rotating bodies.

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Solution K3-28 is a device consisting of a rectangular or circular plate that rotates around a fixed axis with a constant angular velocity ω. The axis of rotation can be perpendicular to the plane of the plate and pass through point O, or lie in the plane of the plate. Point M moves along the plate, moving along a straight line or circle. The law of its relative motion is given by the equation s = AM = f(t) (where s is in centimeters, t is in seconds), which is described in table K3. In the figures, point M is depicted in a position at which s = AM is greater than zero. Dimensions b and l are also indicated in table K3 for each image.

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