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 Multiplying unit vectors by scalars: the multiplier changes the length, and the sign indicates the direction.

Unit Vectors

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:

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

Relative Motion – 2D ( Page 72 )

PhET Simulation – Lab Groups Goto PhET 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

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 E / +x W / -x S / -y

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

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!!!

Relative Motion – 2D ( Page 72 )

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 2 nd ( or even 3 rd ) dimension doesn’t disappear (right?)

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 E / +x W / -x S / -y

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 E / +x W / -x S / -y

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.

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 E / +x W / -x S / -y

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

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

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

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

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

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

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

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!!

Homework Pg. 78 ( in text ) - #36

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?

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 )

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 1 st disc off edge of counter – Second person drops 2 nd disc off edge exact moment 1 st 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

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 Lab Counter-Top Origin +x+x +y+y

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? +x+x +y+y wind

Challenge Question - NOTES