Solution to problem 1.1.18 from the collection of Kepe O.E.

In the problem, the projections of the resultant R plane system of converging forces F1, F2 and F3 on the coordinate axes Rx=18H and Ry=24H are known, as well as the projections of the forces F2 and F3 on the same axes: F2x=-9H, F2y=-7H, F3x= 12H, F3y=0. It is necessary to find the force module F1.

To solve the problem, we use the equation of the resultant forces, which allows us to calculate the module F1 from projections on the coordinate axes:

R^2 = F1^2 + F2x^2 + F2y^2 + F3x^2 + F3y^2 + 2F1F2x + 2F1F2y + 2F1F3x + 2F2xF3x + 2F2yF3y

Substituting the known values, we get:

R^2 = F1^2 + (-9H)^2 + (-7H)^2 + (12H)^2 + 0^2 + 2F1(-9H) + 2F1(-7H) + 2F1(12H) + 2 (-9H)(12H) + 2(-7H)(0)

Simplifying the expression, we get:

R^2 = F1^2 - 94H^2 + 24F1H

F1^2 + 24F1H - 94H^2 - R^2 = 0

Calculating the roots of the quadratic equation, we get:

F1 = (-24H + sqrt(24^2H^2 + 4*94H^2 + 4R^2)) / 2

F1 = (-24H + sqrt(2308 + 4R^2)) / 2

F1 = -12H + sqrt(577 + R^2)

Substituting known values, we get the answer:

F1 = -12 * H + sqrt(577 + 18^2 + 24^2)

F1 = -12 * H + sqrt(1349)

F1 = -12 * H + 36.78

F1 ≈ 34.4

Thus, the force modulus F1 is approximately 34.4 N.

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Our digital store offers a solution to problem 1.1.18 from the collection of Kepe O.?. in physics. This solution is based on the equation of the resultant forces and allows us to calculate the force modulus F1 from projections on the coordinate axes Rx and Ry. We provide a reliable solution to the problem, designed in a beautiful html style, which will allow you to quickly find the information you need and easily navigate.

To solve the problem, we use the equation of the resultant forces, which allows us to calculate the module F1 from projections on the coordinate axes. Substituting the known values, we obtain a quadratic equation whose root is the force modulus F1. Calculating the roots of the quadratic equation, we get the answer: the modulus of force F1 is approximately 34.4 N.

Our solution is suitable for pupils and students studying physics at different levels, and can be used as additional material to improve their knowledge in physics. By purchasing our product, you will receive a reliable and accurate solution to problem 1.1.18 from the collection of Kepe O.?. in a beautiful html design, which will make the learning process more fun and interesting.

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This product is a solution to problem 1.1.18 from the collection of Kepe O.?. The task is to determine the modulus of force F1 of a plane system of converging forces F1, F2 and F3, if their projections on the coordinate axes Rx and Ry, as well as the projections of forces F2 and F3 on the same axes, are known. In accordance with the conditions of the problem, the projections of the resultant R and the forces F2 and F3 on the coordinate axes are known and equal, respectively: Rx=18H, Ry=24H, F2x=-9H, F2y=-7H, F3x=12H, F3y=0. Solving the problem allows us to determine the force modulus F1, which, according to the answer in the collection, is equal to 34.4.

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