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Two-Dimensional Motion

Two-Dimensional Motion. Inclined Planes. Inclined Planes. A simple block on an incline. 30°. F g. Inclined Planes. B/c the block in on an incline, we adjust our coordinate system to fit the incline. Y. X. 30°. F g. Aligning the X axis with the Incline. Inclined Planes.

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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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