Solution K1-07 (Figure K1.0 condition 7 S.M. Targ 1989)

Solution of problem K1-07 (Figure K1.0 condition 7 S.M. Targ 1989)

Problem K1 has two parts: K1a and K1b, each of which must be solved.

Problem K1a is that point B moves in the xy plane (Figures K1.0 - K 1.9, Table K1), and its movement is described by the equations x = f1(t) and y = f2(t), where x and y are expressed in centimeters and t in seconds. It is necessary to find the equation of the trajectory of the point, determine the speed and acceleration of the point at the time t1 = 1 s, as well as its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. To do this, it is necessary to use the data presented in table K1 and in the figures, where the dependence x = f1(t) is indicated in the figures, and the dependence y = f2(t) is given in table K1 (for figures 0-2 in column 2, for figures 3-6 in column 3, for figures 7-9 in column 4). The figure number is selected by the penultimate digit of the code, and the condition number in table K1 is selected by the last one.

Problem K1b is that a 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, where s is in meters and t is in seconds. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s. It is also necessary to depict 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.

Solution to problems K1-07

(Figure K1.0 condition 7 S.M. Targ 1989)

The solution to problem K1-07, presented in the book by S.M. Targa "Physics Problem Book" consists of two parts: K1a and K1b.

Task K1a

In problem K1a, point B moves in the xy plane along a trajectory described by the equations x = f1(t) and y = f2(t), where x and y are expressed in centimeters and t in seconds. It is necessary to find the equation of the trajectory of the point, determine the speed and acceleration of the point at the time t1 = 1 s, as well as its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. To do this, it is necessary to use the data presented in table K1 and in the figures, where the dependence x = f1(t) is indicated in the figures, and the dependence y = f2(t) is given in table K1 (for figures 0-2 in column 2, for figures 3-6 in column 3, for figures 7-9 in column 4).

Task K1b

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 in meters and t is in seconds. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s. It is also necessary to depict 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.

The presented solution to problem K1-07 includes a description of its two parts, K1a and K1b, and contains a detailed description of the problems and their solutions. The description uses beautiful html design, which makes it more attractive and readable for users.

The solution to K1-07 is a problem from the physics problem book by S.M. Targa, which consists of two parts: K1a and K1b.

Problem K1a is that point B moves in the xy plane along a trajectory described by the equations x = f1(t) and y = f2(t), where x and y are expressed in centimeters and t in seconds. It is necessary to find the equation of the trajectory of the point, determine the speed and acceleration of the point at the time t1 = 1 s, as well as its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. To solve the problem it is necessary to use the data presented in table K1 and in the figures. Problem K1b is that a point moves along a circular arc of radius R = 2 m according to the law s = f(t), where s is in meters and t is in seconds. It is necessary to determine the speed and acceleration of the point at the moment t1 = 1 s, and also depict the 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.

To solve the problem, you must use data from table K1 and the figures presented in the book. Problem K1a is solved by finding the derivatives of the equations x(t) and y(t), as well as the tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. Problem K1b is solved by finding the derivatives of the equation s(t) and determining the speed and acceleration of the point at time t1 = 1 s, as well as depicting the vectors v and a in the figure.

The solution to problem K1-07 is presented in the book by S.M. Targa in the form of a text description and schematic drawings. The description of task K1-07 has a beautiful html design, which makes it more attractive and readable for users.

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Solution K1-07 is a problem from the problem book by S.M. Targa, published in 1989. The task consists of two parts - K1a and K1b.

In problem K1a, point B moves in the xy plane along a trajectory specified by the equations x = f1(t) and 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, determine the speed and acceleration of the point at the time t1 = 1 s, as well as the 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 table K1. The figure number is selected by the penultimate digit of the code, and the condition number in table K1 is selected by the last digit.

In problem K1b, a 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 the 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. In the figure, it is necessary to depict the vectors v and a, assuming that the point at this moment is in position M, and the positive direction of reference s is from A to M.

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