Inclined Planes

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## Inclined Planes

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**Inclined Planes**• Label the direction of N and mg. N θ mg Use slide show mode (press F5) for animations.**Inclined Planes**• Mark the direction of acceleration a. N a θ mg**Inclined Planes**• Choose the coordinate system with x in the same or opposite direction of acceleration and y perpendicular to x. y N x a θ mg**Inclined Planes**• Now some trigonometry y N x a θ 90- θ mg θ**Inclined Planes**• Replace the force of gravity with its components. y N x a mg sinθ mg cosθ θ θ mg**Inclined Planes**• Use Newton’s second law for both the x and y directions y N x a mg sinθ mg cosθ θ θ mg The force and acceleration in the x-direction have a negative sign because they point in the negative x-direction.**y**N x a mg sinθ mg cosθ θ θ mg Inclined Planes • Why is the component of mg along the x-axis –mgsinθ • Why is the component of mg along the y-axis –mgcosθ**Inclined Planes**• Why is the component of mg along the x-axis: –mgsinθ • Why is the component of mg along the y-axis: –mgcosθ y N a mg sinθ x θ θ mg mg cosθ**θ**Inclined Planes • Why is the component of mg along the x-axis: –mgsinθ • Why is the component of mg along the y-axis: –mgcosθ y N a mg sinθ x θ mg mg cosθ**θ**Inclined Planes • Why is the component of mg along the x-axis: –mgsinθ • Why is the component of mg along the y-axis: –mgcosθ y opposite N sinθ = a hypotenuse adjacent cosθ = mg sinθ hypotenuse x θ mg mg cosθ