Solution K1-38 (Figure K1.3 condition 8 S.M. Targ 1989)

Solution of problem K1-38 (Figure K1.3, condition 8 S.M. Targ, 1989)

Under number K1 there are two tasks: K1a and K1b, which need to be solved.

Task K1a:

Point B moves in the xy plane (Fig. K1.0 - K1.9, Table K1), and its trajectory in the figures is shown conventionally. The equations of motion of a point are given as follows: x = f1(t), y = f2(t), where x and y are expressed in centimeters, and t in seconds. It is necessary to find the equation of the point's trajectory; 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 dependence y = f2(t) is in column 2, for Fig. 3-6 - in column 3, and for fig. 7-9 - in column 4. As in tasks C1-C4, 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.

Task K1b:

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 beginning 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.

This digital product is a solution to problem K1-38 from the famous textbook “Problems in General Physics” by author S.M. Targa. In problem K1a, you need to find the equation of the trajectory of a point, its speed, acceleration, tangential and normal accelerations and radius of curvature at a given moment in time. In problem K1b, it is necessary to determine the speed and acceleration of a point at time t1 = 1 s on a circular arc.

This is a useful and practical product for students studying general physics and solving problems involving the motion of bodies. The solution is presented in a beautifully designed html format, which makes it easy to read and study the material. In addition, the drawings attached to the solution will help to better imagine the movement of the body and solve the problem. Once you have this solution, you can easily understand and apply the concepts of kinematics and dynamics in your study assignments.

Solution K1-38 from the textbook by S.M. Targa, published in 1989, is a description of the solution to two problems K1a and K1b.

Problem K1a is that point B moves in the xy plane with a given law of motion 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 also determine the speed and acceleration of the point at time t1 = 1 second, the tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. To do this, use the data indicated in Figures K1.0-K1.9 and in Table. K1, where the dependence y = f2(t) is given in columns 2-4 depending on the figure. 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.

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 the distance of the point from some origin A, measured along the circular arc, and t is time. It is necessary to find the speed and acceleration of the point at the time t1 = 1 second and 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. Data for solving this problem are also presented in table. K1.

With this solution, students and general physics students will be able to easily understand and apply the concepts of kinematics and dynamics in their study assignments. The solution is presented in a beautifully designed html format, which makes it easy to read and study the material. The drawings attached to the solution will help you better imagine the movement of the body and solve the problem.

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Solution K1-38 consists of two problems: K1a and K1b. In problem K1a, it is necessary to find the equation for the trajectory of point B, which moves in the xy plane along the given coordinate dependencies x = f1(t) and y = f2(t), where t is time, and x and y are expressed in centimeters. You also need to determine the speed and acceleration of point B at time t1 = 1 s, 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 presented in the figures, and the dependence y = f2(t) is given in Table K1.

In problem K1b, point B 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 the beginning A, measured along the circular arc, and t is time in seconds. It is necessary to determine the speed and acceleration of point B at time t1 = 1 s. It is also necessary to depict the velocity and acceleration vectors in the figure, assuming that point B at this moment is in position M, and the positive direction of reference s is from A to M.

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