Figure 28 shows forces 𝐅1 and 𝐅2 applied to an object O. The resultant force 𝐑 is vertical. Fig.

step 1 In the question, the even figure is drone like this. This is 20 kg. This is f1. This is f2. This

Figure 28 shows forces 𝐅1 and 𝐅2 applied to an object O. The...

Figure 28 shows forces $\mathbf{F}_{1}$ and $\mathbf{F}_{2}$ applied to an object $\mathrm{O}$. The resultant force $\mathbf{R}$ is vertical.
Fig. 28
Determine the magnitude of $\mathbf{R}$ if $\mathbf{F}_{1}$ has a magnitude of $12 \mathrm{kN}$.

Key Concepts

Trigonometric Relationships

Trigonometric relationships, such as sine and cosine functions, are applied to resolve a force into its components or to relate the components back to the original force’s magnitude and direction. These relationships are foundational in solving problems where forces are not aligned with the coordinate axes.

Resultant Force Calculation

The calculation of a resultant force involves summing the individual force vectors, often by combining their resolved components along standard axes. This requires using trigonometric relationships to accurately combine the forces and determine the magnitude and direction of the resultant force.

Equilibrium of Components

Equilibrium of components is a concept used when the resultant force in one direction, such as horizontal, is zero. This indicates that the sum of the forces’ horizontal components cancels out, enabling the resultant force to be purely in another direction, such as vertical.

Force Resolution

Force resolution refers to the method of decomposing a force into its orthogonal components, typically along the horizontal and vertical axes. This decomposition is crucial when dealing with forces applied at angles, as it allows one to analyze and sum the individual components effectively.

Vector Addition

Vector addition is the process of combining multiple forces, taking into account both their magnitudes and directions, to produce a single resultant force. This technique often involves breaking forces into components along chosen perpendicular axes (such as horizontal and vertical) and then using these components to determine the overall effect on an object.

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