Find the angle between the forces given the magnitude of...

Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive $x$ -axis and force 2 as a vector at an angle $\theta$ with the positive $x$ -axis.). Force 1:45 pounds Force 2:60 pounds Resultant Force:90 pounds

Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive $x$ -axis and force 2 as a vector at an angle $\theta$ with the positive $x$ -axis.).
Force 1:45 pounds
Force 2:60 pounds
Resultant Force:90 pounds

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Key Concepts

Resultant Force

The resultant force is the single force obtained from the vector addition of all the forces acting on a body. Its magnitude and direction encapsulate the net effect of these forces, making it crucial for understanding the motion or equilibrium of the object.

Vector Representation

In physics, forces are represented as vectors, which are mathematical objects having both magnitude and direction. This allows us to represent each force in a coordinate system, such as by expressing one force along the positive x-axis and another at an angle, to analyze their combined effect.

Vector Addition

When multiple forces act on an object, their combined effect is determined by vector addition. This involves adding the corresponding components of each force to yield a resultant force, the overall force acting on the object.

Law of Cosines

The law of cosines is a mathematical tool used to relate the sides and angles of a triangle. In the context of forces, it is applied to the triangle formed by the two force vectors and their resultant. This allows for determining the angle between the original forces when the magnitudes of the forces and their resultant are known.

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