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Physics 1110: Mechanics

• Tutorial pretest due at 4pm today

• Tutorials tomorrow in G2B60, G2B75, & G2B77

Web page: http://www.colorado.edu/physics/phys1110/

Announcements:

• CAPA assignments will be in bins in G2B hallway after lecture

• Due to Labor Day holiday, 1st CAPA set will be due Wednesday at 10pm

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Tutorials

Click on Instructors link to find out which room you should go to. You need to know your section number.

There is also a link to a map showing the room locations

Tomorrow you will spend most of the time taking the FMCE (Force and Motion Conceptual Evaluation). This is a diagnostic tool only used to determine your initial physics knowledge. It does not affect your grade (but please do your best).

After the exam you will start working on Representations of Motion tutorial but you will need to finish it on your own.

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Honors co-seminar

Open to students taking at least Calc 2 but is intended for physical science, engineering or mathematics majors; especially physics, astrophysics and engineering physics.

There are ~5 spots still open in a 1 credit coseminar.

Deeper study of PHYS1110 ideas. Involves investigating problems with analytical & numerical methods, discussion of historical foundations, individual & group projects, writing assignments, and presentations.

More information at www.colorado.edu/physics/honr1001

If interested contact Paul Beale by visiting in physics department office, email at Paul.Beale@Colorado.edu, or call 303-492-0297.

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Thinking about motion

Our first project is to observe and think about motion

We see many examples of motion in the world around us.

We are going to try to break down exactly what we mean by motion.

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Motion diagram

If you imagine doing the same thing while I walk across the stage and then drawing it you might get a motion diagram…

. . . . .

If you imagine filming a long jump and then putting all of the frames together you might get…

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If instead of walking across the stage I stroll the first half and run the second half (in the same direction as before) what will the motion diagram look like?

Clicker question 1 Set frequency to BA

. . . . .

. . . . .

. . . . .

.

.

A.

B.

C.

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Particle model

Although a person is an extended object, for now we model everything as a particle.

. . . . ..

We need to label the points to know the order of events (which gives us the direction of motion).

10 2 3 4 5

Looking at the diagram can one tell the direction of motion?

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Measuring positionWe have the positions of the professor at 6 different times

To complete this picture we need a coordinate system

A coordinate system needs an origin.This is arbitrary but the starting location is a good choice

A coordinate system needs axes.With only 1 dimension, we just need one axis.

x10 2 3 4 5

A position vector gives a location relative to the originOne example is the position vector

r

4r

4r

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Vectors• Vectors have magnitude and direction

– velocity, acceleration, displacement, force

• Scalars only have magnitude– speed, temperature, mass, volume

• Vector quantities are indicated by an arrow above them:

• Can use arrow to represent direction & magnitude r

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Draw an arrow from tail of to tip of :

Place the tail of at the tip of :

Graphical vector additionWant to find where andBAC

A

B

Vector subtraction is done by adding the negative. The negative of a vector has the same length but opposite direction.

BABA

A

B

Start with A

A

B

A

B

BAC

A

BA B

BAC

This is

BA

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Clicker question 2 Set frequency to BA

Q. Three vectors, are shown. Which answer represents the vector ?

CBA

,,

CBAS

(A) (B) (C) (D)(E) None of these.

A B

C

A

B

C

S

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Follow the HOP to the 29th Street Mall

Canyon Fol

som

Colorado

21

0

2r

1r

0r

Origin at Duane physics

Start at Geology buildingDown to Arapahoe and then the mall

r

Position vectors for each point

Displacement vectors between points

Note that and so 10 rrr

01 rrr

Position vectors give the location of points from an origin.

Displacement vectors go from a start point to an end point (and so they don’t depend on the origin location).

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Distance versus Displacement

Canyon Fol

som

Colorado

21

0

r

The displacement vector between point 0 and point 2 is

Since it is a vector, it has a magnitude and direction.

We also define the distance as the ground covered by the actual route.

02 rrr

The distance is a scalar. It does not give a direction.

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An object’s velocity tells us the speed and direction of motion

An object’s speed tells how fast it is moving and is a scalar

travelof interval time traveleddistance speed average

A displacement vector gives the change in position: if rrr

Defining velocityBack to the position of the professor at 6 different times

This occurs over some time interval:

x0r

1r

2r

3r

4r

if ttt

interval timentdisplaceme

velocity average trv

avg

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The length of the velocity vector tells us the average speed between the two points

Adding velocity to motion diagramsNote that the velocity vector points in the same direction as the displacement vector.

x0v

1v

2v

3v

4v

trv

avg

If all of the time intervals in a motion diagram are the same (as we have specified so far) then the velocity vector length is proportional to the displacement vector length.

So the vectors connecting points are also velocity vectors: