Solution K1-33 (Figure K1.3 condition 3 S.M. Targ 1989)

The solution to problem K1-33 (Figure K1.3 condition 3 S.M. Targ 1989) includes two problems K1a and K1b that need to be solved.

The task of K1a is as follows. Point B moves in the xy plane (Fig. K1.0 - K 1.9, Table K1), where the trajectory of the point in the figures is shown conventionally. The law of motion of a point is given by the equations: x = f1(t), y = f2(t), where x and y are expressed in centimeters, t in seconds. It is necessary to find the equation of the trajectory of the point, and for the moment of time t1 = 1 s, determine the speed and acceleration of the point, as well as its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. The dependence x = f1(t) is indicated directly in the figures, and the dependence y = f2(t) is given in the table. K1 (for Fig. 0-2 in column 2, for Fig. 3-6 in column 3, for Fig. 7-9 in column 4). The figure number is selected according to the penultimate digit of the code, and the condition number in the table. K1 - according to the last one.

The task of K1b is as follows. The point moves along a circular arc of radius R = 2 m according to the law s = f(t), given in table. K1 in column 5 (s - in meters, t - in seconds), where s = AM is the distance of a point from some origin A, measured along the arc of a circle. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s. Draw vectors v and a in the figure, assuming that the point at this moment is in position M, and the positive direction of reference s is from A to M.

This digital product is a solution to problem K1-33 from the textbook “Problems in General Physics” edited by S.M. Targa, released in 1989. The solution includes two problems K1a and K1b, for which detailed instructions and data tables are provided.

For problem K1a, it is necessary to find the equation of the trajectory of a point, as well as the speed, acceleration, tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory at time t1 = 1 s. For problem K1b, it is necessary to determine the speed and acceleration of the point at time t1 = 1 s and depict the vectors v and a in the figure.

The solution is presented in a beautiful html design that preserves the structure of the original textbook, which ensures convenience and comfort when reading and using this digital product.

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Solution K1-33 consists of two problems: K1a and K1b.

In problem K1a, it is necessary to find the equation for the trajectory of point B moving in the xy plane according to the law x = f1(t), y = f2(t). For the moment of time t1 = 1 s, it is necessary to determine the speed and acceleration of the point, as well as its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. The dependence y = f2(t) is given in tabular form in table. K1, and the dependence x = f1(t) is indicated directly in the figures.

In problem K1b, a point moves along a circular arc of radius R = 2 m according to the law s = f(t), where s is the distance of the point from some origin A, measured along the circular arc. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s, and also draw vectors v and a in the figure, assuming that the point at this moment is in position M, and the positive direction of reference s is from A to M. Dependence s = f(t) is also given in tabular form in Table. K1.

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