Two forces of 255 N and 325 N act on an object. The angle between the forces is 64^∘ . Find the

step 1 In this question we have been provided with the two forces that are acting on the body at 64 deg

Two forces of 255 N and 325 N act on an object. The angle...

Two forces of $255 \mathrm{N}$ and $325 \mathrm{N}$ act on an object. The angle between the forces is $64^{\circ} .$ Find the magnitude of the resultant and the angle that it makes with the smaller force.

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Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to determine a single, resultant vector. In the context of forces, it involves both magnitude and direction, and it is essential for understanding the net effect when multiple forces act on an object simultaneously.

Resultant Force

The resultant force is the single force that represents the combined effect of two or more forces acting on an object. Determining its magnitude and direction can simplify the analysis of the motion or equilibrium of objects under multiple influences.

Law of Cosines

The Law of Cosines is a trigonometric principle used to calculate the length of a side in a triangle when two sides and the included angle are known. In vector addition problems, it is particularly useful for finding the magnitude of the resultant force when the forces are not perpendicular.

Law of Sines

The Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles. It is used in vector analysis to determine unknown angles in the triangle formed by force vectors, such as the orientation of the resultant force relative to one of the original forces.

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