An object of mass m=5.95 kg has an acceleration 𝐚=(1.17 m / s^2) 𝐱̂+(-0.664 m / s^2) 𝐲̂ . Three

An object of mass m=5.95 kg has an acceleration 𝐚=(1.17 m /...

An object of mass $m=5.95 \mathrm{kg}$ has an acceleration $\overrightarrow{\mathbf{a}}=\left(1.17 \mathrm{m} / \mathrm{s}^{2}\right) \hat{\mathbf{x}}+\left(-0.664 \mathrm{m} / \mathrm{s}^{2}\right) \hat{\mathbf{y}}$ . Three forces act on this object: $\overrightarrow{\mathbf{F}}_{1}, \overrightarrow{\mathbf{F}}_{2},$ and $\overrightarrow{\mathbf{F}}_{3}$ . Given that $\overrightarrow{\mathbf{F}}_{1}=(3.22 \mathrm{N}) \hat{\mathbf{x}}$ and $\overrightarrow{\mathbf{F}}_{2}=(-1.55 \mathrm{N}) \hat{\mathbf{x}}+(2.05 \mathrm{N}) \hat{\mathbf{y}},$ find $\overrightarrow{\mathbf{F}}_{3}$

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Key Concepts

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = m * a). This principle is fundamental for determining unknown forces when the mass and acceleration of an object are known, as it links the dynamics of motion directly with the forces applied to the object.

Vector Addition of Forces

When multiple forces act on an object, their combined effect is found by vector addition. This means summing the forces component by component, which requires handling both magnitude and direction. Vector addition is essential for understanding how different forces interact to produce a net force that causes acceleration.

Force Decomposition

Force decomposition involves breaking a force down into its perpendicular components, usually along the x and y axes. This method simplifies the analysis of forces acting in multiple dimensions by allowing each component to be considered separately, which is critical in applying Newton’s second law and solving for unknown forces.