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Two-Dimensional Motion

This guide explores the dynamics of a block resting on a 30° inclined plane. It explains how forces act on the block, specifically focusing on gravitational force (Fg) and its components, including Fgx, which pulls the block down the incline, and Fgy, which maintains contact with the plane. Key concepts include adjusting the coordinate system to match the incline and solving for the force components using right triangle relationships. A real-world example involves a skier on a 35° slope, analyzing forces and creating diagrams to visualize the problem.

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Two-Dimensional Motion

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  1. Two-Dimensional Motion Inclined Planes

  2. Inclined Planes A simple block on an incline 30° Fg

  3. Inclined Planes B/c the block in on an incline, we adjust our coordinate system to fit the incline Y X 30° Fg Aligning the X axis with the Incline

  4. Inclined Planes • Notice the gravitational force (Fg) is pulling straight down • Doesn’ t the Fg also pull you down the hill? YEP! So, there are components of the Fg (x and y)

  5. Inclined Planes • There is an Fgx and an Fgy Fgx Fgy Fg

  6. Inclined Planes • Notice that the coordinate system has been adjusted… How much? Y X 30° Fg It has been adjusted by the incline, 30°

  7. Inclined Planes • Therefore the angle between Fg and Fgy is… 30° Fgx Fgy 30° Fg

  8. Inclined Planes • Therefore the angle between Fg and Fgy is… 30° Fgx Fgy 30° 30° Fg

  9. Inclined Planes • Now we are able to solve for fgx and fgy • Fgx is the force pulling the block down the incline • Fgy is the force keeping the block in contact with the incline

  10. Inclined Planes • Realign the vectors (Tip-to-Tail) to complete a right triangle and you get… Fgy 30° Fg 30° Fgx

  11. Inclined Planes • Lets take a closer (magnified) look at the similar triangle Fgy 30° Fg 30° Fgx

  12. Inclined Planes • Lets take a closer (magnified) look at the similar triangle Y Nice! Fgy 30° Fgx X Fg

  13. Inclined Plane Problem • A 784-N skier on a hill that makes a 35 angle with the horizontal begins to accelerate down the hill. • Draw the pictorial diagram and free-body diagram • What is the component of the skier’s weight parallel to the incline plane? • What is the normal force?

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