Tasks on finding of equally effective two forces meet in vector algebra and in theoretical mechanics. Force is size vector, and at summation of forces it is necessary to consider its direction.
It is required to you
- - handle;
- - pencil;
- - ruler;
- - protractor;
- - calculator;
- - note paper.
Instruction
1. In theoretical mechanics force is considered as the sliding vector. T. e, a vector of forces it is possible to transfer along straight lines on which they are located. Therefore, the directions of two forces applied to a body are crossed in a point And. If on a statement of the problem you need to find the equally effective two forces operating on a body along one straight line, then scalar values of multidirectional forces are subtracted. And forces applied in one direction develop.
2. Other case is when two forces affect a body at an angle to each other. To put forces in this example, it is necessary to know a corner between their vectors. It is possible to find equally effective forces a graphic and graphic-analytical method.
3. The graphic method of a vector develops by the rule of a parallelogram or triangle. For example, two strength 5.5H and 11.5H are given, the corner between them is equal to 65 lakes. To find equally effective forces, at first choose the scale of creation of the schedule. For example, 1 cm = 1H. From a point And at an angle 65o to each other postpone a vector an equal to 5.5 cm, and b equal to 11.5 cm. By the rule of a parallelogram draw a total vector of two forces. Its length in this scale equals the scalar size of net force - 14.5H. To put forces by a graphic method by the rule of a triangle, place the beginning of the second vector in the end of the first. Construct a triangle. Length of the party in this scale is a scalar size of the sum of forces.
4. At composition of two forces by a graphic-analytical method you can not observe scale at creation of the drawing. Construct a triangle or a parallelogram similar to a step 3. According to the theorem of cosines find the party of a triangle the EXPERT or the diagonal of a parallelogram: c = (b^2+a^2-2bc cosb) ^1/2; where a, b are scalar sizes of vectors of two applied forces, b is a corner between them in a triangle. Apparently from the drawing, b corner = 180-a.