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09/25/12 - Bellwork

09/25/12 - Bellwork. What is position, displacement, speed, velocity, and acceleration?. NOTES. Unit Vectors Position, Displacement, Velocity, and Acceleration Vectors. 3-4 Unit Vectors. Unit vectors are dimensionless vectors of unit length. 3-4 Unit Vectors.

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09/25/12 - Bellwork

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  1. 09/25/12 - Bellwork What is position, displacement, speed, velocity, and acceleration?

  2. NOTES • Unit Vectors • Position, Displacement, Velocity, and Acceleration Vectors

  3. 3-4 Unit Vectors Unit vectors are dimensionless vectors of unit length.

  4. 3-4 Unit Vectors Multiplying unit vectors by scalars: the multiplier changes the length, and the sign indicates the direction.

  5. Unit Vectors

  6. Relative Motion - 1D ( Page 71 ) The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds:

  7. Relative Motion – 2D ( Page 72 ) Passenger relative to ground = passenger-train + train-ground

  8. Relative Motion – 2D ( Page 72 )

  9. PhET Simulation – Lab Groups • GotoPhET website • Search for “Motion in 2D” • Make sure “Show Both” is selected at top • Which is the Green Vector ; which is the Blue Vector? • If the Labtop Screen represents an x-y axis, visualize the two components of each

  10. Bellwork – 09/27/12 • you walk “in town” and you walk 0.45 m to the West and turn to walk 0.35 m to the North • Picture this in an x-y coordinate system • Write the displacement vector in unit vector notation N / +y W / -x E / +x S / -y

  11. Bellwork – 09/27/12 N / +y W / -x E / +x S / -y

  12. NOTES – 09/27/12 • Unit Vectors • Position, Displacement, Velocity, and Acceleration Vectors • WE ARE TALKING ABOUT 2-DIMENSIONS • Vertical AND Horizontal • LET’S DO IT!!!

  13. Relative Motion – 2D ( Page 72 )

  14. 1D Unit Vector Notation? The speed of the passenger with respect to the ground depends on the relative directions of the passenger’s and train’s speeds: Motion only in one direction, but the 2nd ( or even 3rd ) dimension doesn’t disappear (right?)

  15. Bellwork Question • you walk “in town” and you walk 0.45 m to the West and turn to walk 0.35 m to the North • Picture this in an x-y coordinate system • What is the distance traveled? N / +y W / -x E / +x S / -y

  16. Bellwork Question • you walk “in town” and you walk 0.45 m to the West and turn to walk 0.35 m to the North • Picture this in an x-y coordinate system • What is the distance traveled? In Green • 0.80 m N / +y W / -x E / +x S / -y

  17. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Position vector points from the origin to the location in question. The displacement vector points from the original position to the final position.

  18. Bellwork Question • you walk “in town” and you walk 0.45 m to the West and turn to walk 0.35 m to the North • Picture this in an x-y coordinate system • Initial Position? • Final Position? N / +y W / -x E / +x S / -y

  19. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Average velocity vector: (3-3) So is in the same direction as .

  20. Bellwork Question N / +y W / -x E / +x S / -y

  21. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Instantaneous velocity vector is tangent to the path:

  22. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Average acceleration vector is in the direction of the change in instantaneous velocity:

  23. Acceleration Vectors • So when considering an acceleration vector, are we using two average or instantaneous velocities?

  24. Acceleration Vectors • So when considering an acceleration vector, are we using two average or instantaneous velocities?

  25. 3-5 Position, Displacement, Velocity, and Acceleration Vectors Velocity vector is always in the direction of motion; acceleration vector can point anywhere:

  26. 2D Motion PhET Simulation • Lab Groups – Going to devise more variety of groups ( partners, groups of 3, etc. ) • Remember the acceleration vector would go crazy, eventually point in opposite direction when you would reverse the direction of the “object” ( or dot on the screen ) • Check it out again!!

  27. Homework • Pg. 78 ( in text ) - #36

  28. 2D Motion – Mini-Lab Activity • Everybody answers questions ( NAME!! ) • Separate sheet of paper – will use for QUIZ also • Preliminary Question: If you slide a coin off the edge of the lab-station counter-top, is there any interdependence between the vertical and horizontal motion?

  29. 2D Motion – Mini-Lab Activity • Preliminary Question: If you slide a coin off the edge of the lab-station counter-top, is there any interdependence between the vertical and horizontal motion? • They are independent of each other, or one is not dependent on the other ( two ways to state it )

  30. 2D Motion – Mini-Lab Activity • Procedure – Go to lab station with two discs • Hanging masses ( up front ) • Must be the same mass!! • One person slides 1st disc off edge of counter • Second person drops 2nd disc off edge exact moment 1st disc leaves the edge • Must measure/estimate counter height and distance sliding discs lands away from counter • Other group members observe ( see / listen ) when each disc lands

  31. 2D Motion – Mini-Lab Activity • Questions: • 1] Did the discs land at the same time ( after leaving the edge of the lab counter )? • 2] Sketch a graph of the “sliding” disc’s motion • Formulate an equation ( y as a function of x ) for this motion with the edge of the floor being the coordinate system origin • Make +x point away from counter +y Lab Counter-Top Origin +x

  32. Challenge Question - NOTES • PROBLEM: You drop a paper-wad off a bridge ( releasing it from rest ). The wind is blowing CONSTANTLY ( in the +x direction ) at 1.0 m/s. The paper-wad lands on the ground with a vertical velocity of – 3.0 m/s ( air resistance is very much there so not just gravity affecting it ) after 2.0 sec. • Q1: What is the velocity vector when it lands? • Q2: What is the acceleration vector? +y wind +x

  33. Challenge Question - NOTES

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