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More 2D Motion: On a Ramp and Relative

More 2D Motion: On a Ramp and Relative More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: More 2D Motion: On a Ramp and Relative

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More 2D Motion: On a Ramp and Relative

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  1. More 2D Motion: On a Ramp and Relative

  2. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall:

  3. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall:

  4. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: afreefall = 9.8 m/s2 (down)

  5. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: afreefall = 9.8 m/s2 (down) This is the only acceleration causing the cart to roll—if there were no gravity then the cart would stand still!

  6. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: Let’s now break afreefall into two component vectors: one parallel to the ramp and one perpendicular to the ramp. afreefall = 9.8 m/s2 (down) This is the only acceleration causing the cart to roll—if there were no gravity then the cart would stand still!

  7. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: Let’s now break afreefall into two component vectors: one parallel to the ramp and one perpendicular to the ramp. afreefall = 9.8 m/s2 (down) This is the only acceleration causing the cart to roll—if there were no gravity then the cart would stand still!

  8. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: afreefall = 9.8 m/s2 (down)

  9. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: Only the parallel [green] component causes motion along the ramp. afreefall = 9.8 m/s2 (down)

  10. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: Only the parallel [green] component causes motion along the ramp. afreefall = 9.8 m/s2 (down) Similar Triangles!

  11. More 2D Motion: On a Ramp and Relative The acceleration vector that causes an object to slide down a ramp is not the full acceleration of an object in freefall: Only the parallel [green] component causes motion along the ramp. θ afreefall = 9.8 m/s2 (down) θ Similar Triangles!

  12. y ax = afreefall• sin (θ) ax θ x afreefall = 9.8 m/s2 (down) θ

  13. y ax = afreefall• sin (θ) Example: if θ = 20° then ax = 9.8 m/s2 (0.342) = 3.4 m/s2 ax θ x afreefall = 9.8 m/s2 (down) θ

  14. y ax = afreefall• sin (θ) Example: if θ = 20° then ax = 9.8 m/s2 (0.342) = 3.4 m/s2 ax θ x afreefall = 9.8 m/s2 (down) θ Motion on the ramp involves the 1D equations of motion, with ax given in terms of angle θ (as given above).

  15. Relative Motion

  16. Relative Motion —all motion is relative to some reference point.

  17. Relative Motion —all motion is relative to some reference point. Example: you throw a ball up as you run at a constant velocity…

  18. Relative Motion —all motion is relative to some reference point. Example: you throw a ball up as you run at a constant velocity… Relative to you the ball goes up and down…relative to a stationary observer the ball moves along a parabolic curve.

  19. Relative Motion —all motion is relative to some reference point. Example: you throw a ball up as you run at a constant velocity… Relative to you the ball goes up and down…relative to a stationary observer the ball moves along a parabolic curve. Think of a similar example: when you throw something up in a moving car.

  20. Think of an example when the moving thing is not a car but a river. You row a boat across the river but the river is moving… BOAT Your motion relative to the river… The river’s motion relative to someone on shore… Your motion relative [as seen by] someone on shore.

  21. Think of an example when the moving thing is not a car but a river. You row a boat across the river but the river is moving… A sum of displacement vectors. BOAT Your motion relative to the river… The river’s motion relative to someone on shore… Your motion relative to [“as seen by”] someone on shore.

  22. Think of an example when the moving thing is not a car but a river. You row a boat across the river but the river is moving… A sum of velocity vectors. BOAT Your velocity relative to the river… The river’s velocity relative to someone on shore… Your velocity relative to [“as seen by”] someone on shore.

  23. Example problems form the textbook: Problems 17, 22 and 29 done in class.

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