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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
2
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.
3
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 [email protected], or call 303-492-0297.
4
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.
5
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…
6
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.
7
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?
8
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
9
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
10
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
11
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
12
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).
13
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.
14
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: