Solution K1-76 (Figure K1.7 condition 6 S.M. Targ 1989)

Solution of problem K1-76 (Figure K1.7, condition 6, S.M. Targ, 1989)

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

Problem K1a. Point B moves in the xy plane (the trajectory of the point is shown conventionally in Figures K1.0 - K1.9, Table K1). 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, and t in seconds. It is necessary to find the equation of the trajectory of the point, as well as the speed and acceleration of the point at the time t1 = 1 s. You also need to find the tangent and normal acceleration of the point and the radius of curvature at the corresponding point on 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 figures 0-2, column 2 is used, for figures 3-6 - column 3, and for figures 7-9 - column 4. The figure number is selected by the penultimate digit of the code, and the condition number in the table. K1 - according to the last one.

Problem K1b. The point moves along a circular arc of radius R = 2 m with the law of motion 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.

Welcome to our digital goods store! We are pleased to offer you a digital solution to problem K1-76, based on condition 6 from the book by S.M. Targa 1989 and presented in Figure K1.7.

The solution contains two problems: K1a and K1b, each of which is presented in a beautifully designed html format. In problem K1a, it is necessary to find the equation of the trajectory of a point, speed, acceleration, tangential and normal accelerations and the radius of curvature of the point at the corresponding point of the trajectory. In problem K1b, you need to determine the speed and acceleration of a point at time t1 = 1 s and depict vectors v and a in the figure.

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Solution K1-76 is a problem that consists of two subtasks: K1a and K1b. Subtask K1a is that point B moves in the xy plane along a certain 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, and also determine the speed and acceleration of the point at the time t1 = 1 s, its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory.

Subtask K1b is that 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 - distance

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