Resultant Force Two forces of magnitude 30 newtons (N) and 70 N act on an object at angles of 4

step 1 My friends, this is the problem based on addition of vectors. Here it is given two forces having

Resultant Force Two forces of magnitude 30 newtons (N) and...

Resultant Force Two forces of magnitude 30 newtons (N) and $70 \mathrm{~N}$ act on an object at angles of $45^{\circ}$ and $120^{\circ}$ with the positive $x$ -axis, as shown in the figure. Find the direction and magnitude of the resultant force; that is, find $\mathbf{F}_{1}+\mathbf{F}_{2}$.

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Key Concepts

Force as a Vector

Forces are vector quantities, which means they have both magnitude and direction. This concept is essential for understanding how different forces affect an object, as each force can be represented by an arrow in a coordinate system.

Vector Addition

Vector addition is the process of combining two or more vectors to determine a single resultant vector. This involves adding corresponding components of each vector, which allows for a comprehensive understanding of the net effect of multiple forces acting on an object.

Decomposition of Vectors into Components

Decomposing a vector into its x and y components involves using trigonometric functions such as sine and cosine to break down the vector along the coordinate axes. This technique simplifies the process of vector addition by allowing each component to be handled separately.

Trigonometric Functions in Vector Analysis

Trigonometric functions, particularly sine and cosine, are used to relate the magnitude and direction of a vector to its components. They are crucial when converting between polar and rectangular representations, assisting in accurately computing the resultant force.

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