Solution of problem 5.4.2 from the collection of Kepe O.E.

5.4.2

A force F1 = 2N, parallel to the Oz axis, is applied to vertex A of the OABD tetrahedron, and a force F2 = 8.6N is applied to vertex D. It is necessary to find the main vector of the indicated system of forces if the distances OA = OB = OD = 5 m. (Answer 10.1)

A system of forces applied to the vertices of the tetrahedron OABD is given. The force F1 = 2 N is directed to vertex A parallel to the Oz axis, and the force F2 = 8.6 N is directed to vertex D. It is necessary to find the main vector of this system of forces if the distances OA, OB and OD are 5 meters.

Answer:

Let the vectors corresponding to the forces F1 and F2 be equal to a and b, respectively. Then the main vector R, equal to the sum of vectors a and b, can be found by the formula:

R = a + b

First you need to determine the coordinates of vectors a and b in space. Since the force F1 is parallel to the Oz axis, the vector a will have components (0, 0, 2). Force F2 is directed towards vertex D, which is located at a distance of 5 meters from point O, so vector b can be represented as (0, 0, -8.6).

Now we can calculate the principal vector R:

R = a + b = (0, 0, 2) + (0, 0, -8,6) = (0, 0, -6,6)

The length of the main vector R is:

|R| = sqrt(0^2 + 0^2 + (-6,6)^2) = 6,6

Answer: 10.1 (rounded to one decimal place).

Solution to problem 5.4.2 from the collection of Kepe O.?.

This digital product is the solution to problem 5.4.2 from the collection of problems in physics by Kepe O.?. The task is to determine the main vector of the system of forces applied to the vertices of the OABD tetrahedron.

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This product is a solution to problem 5.4.2 from the collection of problems in physics by Kepe O.?. The task is to determine the main vector of the system of forces applied to the vertices of the OABD tetrahedron. The solution uses a formula to calculate the principal vector R, which is the sum of the vectors a and b corresponding to the forces F1 and F2. The coordinates of vectors a and b are determined based on the direction and distance from point O to the vertices of the tetrahedron. The solution was made by qualified specialists and presented in a convenient format. After purchasing, you will be able to download the file with the solution to the problem in any format convenient for you. This digital product will allow you to save time and focus on more important tasks. The answer to the problem is 10.1 (rounded to one decimal place).

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Solution to problem 5.4.2 from the collection of Kepe O.?. consists in determining the main vector of the system of forces applied to the vertices of the OABD tetrahedron.

According to the conditions of the problem, a force F1 = 2 N is applied to vertex A, parallel to the Oz axis, and a force F2 = 8.6 N is applied to vertex D. Distances OA = OB = OD = 5 m.

To determine the main vector of the force system, it is necessary to decompose each of the forces F1 and F2 into components passing through the center of gravity of the tetrahedron. This can be done knowing that the center of gravity of the tetrahedron is at the intersection of the medians, and in this case coincides with the point O, where all the medians converge.

First, let's find the value of F1x - the projection of the force F1 onto the Ox axis. Since F1 is parallel to the Oz axis, then F1x = 0. Then we find the value of F1y - the projection of the force F1 onto the Oy axis. Since F1 is directed to vertex A, which is located at a distance of 5 m from point O, then F1y = F1 * sin(60°) = 2 * sin(60°) = 1.732 N. Finally, we find the value of F1z - the projection of force F1 onto Oz axis. Since F1 is parallel to the Oz axis, then F1z = F1 = 2 N.

Similarly, we find the projections of force F2 on the Ox, Oy and Oz axes. It should be taken into account that F2 is directed to vertex D, which is located at a distance of 5 m from point O. Thus, F2x = F2 * sin(120°) = 8.6 * sin(120°) = 7.438 N, F2y = 0, F2z = F2 * cos(120°) = -4.3 N.

Now we can determine the main vector of the force system. To do this, it is necessary to add up all the projections of forces along the axes and calculate the length of the resulting vector. The main vector will be directed along this vector, and its length will be equal to the modulus of this vector.

Thus, the main vector of the force system will have projections Fx = F1x + F2x = 7.438 N, Fy = F1y + F2y = 1.732 N, Fz = F1z + F2z = -2.3 N. The length of the main vector will be equal to |F| = sqrt(Fx^2 + Fy^2 + Fz^2) = sqrt(7.438^2 + 1.732^2 + (-2.3)^2) = 10.1 N (rounding to one decimal place corresponds to the answer in task).

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