Solution to problem 1.3.10 from the collection of Kepe O.E.

1.3.10

To solve the problem, it is necessary to determine the modulus of the resultant of three forces that converge at an angle ?=60°. The moduli of these forces are known and equal to F1=5kN, F2=12kN and F3=9kN.

To solve the problem we use the formula:

F = √(F1^2 + F2^2 + F3^2 + 2*F1*F2*cos(?1-?2) + 2*F2*F3*cos(?2-?3) + 2*F1* F3*cos(?1-?3))

Substituting known values, we get:

F = √(5^2 + 12^2 + 9^2 + 2*5*12*cos(0.°) + 2*12*9*cos(120.°) + 2*5*9*cos(-60.°)) ≈ 20,9 (кН)

Thus, the modulus of the resultant of the three converging forces is about 20.9 kN.

Solution to problem 1.3.10 from the collection of Kepe O..

We present to your attention a digital product - the solution to problem 1.3.10 from the collection of Kepe O.. This product will be useful for students, teachers and everyone who is interested in physics and mathematics.

In this solution you will find a detailed description of the process of solving the problem, as well as the formulas and calculations necessary to solve it. Problem 1.3.10 describes the determination of the modulus of the resultant of three forces that converge at an angle ?=60°, for given moduli of these forces. The solution contains the answer, namely that the modulus of the resultant of the three converging forces is about 20.9 kN.

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Problem 1.3.10 from the collection of Kepe O.?. consists in determining the modulus of the resultant of three forces directed at an angle of 60 degrees to each other and having modules F1 = 5 kN, F2 = 12 kN and F3 = 9 kN, respectively.

To solve the problem, it is necessary to apply the cosine theorem, which allows you to determine the module of the resultant force from the modules and directions of the forces applied to it. According to the cosine theorem, the modulus of the resultant force R can be calculated using the formula:

R = √(F1^2 + F2^2 + F3^2 + 2F1F2cos60° + 2F1F3cosα + 2F2F3cosβ),

where α and β are the angles between vectors F1 and F3, F2 and F3, respectively.

Substituting known values, we get:

R = √(5^2 + 12^2 + 9^2 + 25120.5 + 259cosα + 2129*cosβ) = 20.9 кН.

Thus, the modulus of the resultant of the three forces specified in the problem statement is equal to 20.9 kN.

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