1. Physics 218 Lecture 2
Dr. David Toback
Physics 218, Lecture II

2. Announcements Having trouble getting started on WebCT? Try:
ITS Help sessions
Open access lab/student computing.
Instructions on faculty.physics.tamu.edu/toback/WebCT to
Check your neo account for announcements. Two of you had your bounce
Any Volume 1 of the 11th edition of Young & Freedman will be fine. You will need Volume 2 for Phys208 and Volume 3 for beyond that. The maroon “University Edition” is also fine.
Physics 218, Lecture II

3. Procedure for Each Week
Week 1 (This week):
Lecture: Chapter 1 (Reading, but nothing due)
Recitation: Calculus and Lab Techniques
Homework due: None
Week 2 (Next week):
Homework due (Monday): Math quizzes
Lecture: Chapter 2 (Reading and Lecture Assignment due)
Recitation: Chapter 1 (and Lab 1)
Week 3 (The week after that):
Homework due (Monday): Chapter 1
Lecture: Chapter 3 (Reading and Lecture Assignment due)
Recitation: Chapter 2 (no lab, but lab 1 is due)
Etc..
Physics 218, Lecture II

4. Chapter 1: Math n’ Stuff Won’t cover the entire chapter:
Problem Solving
Tricks
Methods
Vectors
Components (Unit vectors)
Addition
Multiplication (dot and cross products)
Physics 218, Lecture II

5. Physics 218, Lecture II

6. Problem Solving Overview
There are good general problem solving TRICKS
Units checking
Special case checking
Etc.
There are good METHODS of problem solving that prepare you for the exams
We’ll use both to solve
problems in lecture
Physics 218, Lecture II

7. First Things First!
What’s the first thing you should do when you’re given a a problem?
Draw a diagram!!!
Usually good for some partial credit
List givens and wants as variables
Also a good bet for partial credit
Then use reasonable equations and solve with your variables
Trick #1
Physics 218, Lecture II

8. Trick #2: Units
The speed of your car isn’t measured in seconds, its measured in meters/second (or miles/hour etc.)
Paying attention to the units will help you catch LOTS of mistakes on exams, quizzes and homework!!
If we ask what the mass of your car is, make sure your answer is in kg (or lbs etc.)
Trick #2: Every time you finish a problem ALWAYS check the units of your answer!!
Physics 218, Lecture II

9. Tricks #3 and #4 Check Reasonableness:
Can you find another way to do the same problem that gives the same answer?
Simple numbers give expected numerical answers? Example: Zero, or infinity
Trick #3
Trick #4
Physics 218, Lecture II

10. How to use the Tricks and Methods
Next we’ll do an example problem like one of the homework problems in the text book
Solve this problem using the right method
Draw a diagram
Convert the numbers to variables
Solve to get a formula
Plug in the numbers at the end
Check
Reasonable numbers?
Silly numbers?
Another way to do the same problem?
Physics 218, Lecture II

11. Example Problem
You want to measure the height of a building. You stand 2m away from a 3m pole and see that it’s “in line” with the top of the building. You measure 16 m from the pole to the building.
What is the height of the building?
16 m
Physics 218, Lecture II

12. Vectors: Why we care about them Addition & Subtraction Unit Vectors
Multiplication
Physics 218, Lecture II

13. Why do we care about Vectors?
As you may have noticed, the world is not one-dimensional
Three dimensions: X, Y and Z. Example:
Up from us
Straight in front of us
To the side from us
All at 90 degrees from each other. Three dimensional axis.
Need a way of saying how much in each direction
For this we use VECTORS
Physics 218, Lecture II

14. Vectors have a magnitude AND a direction
Vector and Scalar
Vectors have a magnitude AND a direction
I’m driving 70 miles/hr SouthEast to Houston
Scalars are just a number
My speedometer says 70 m/hr
Physics 218, Lecture II

15. Where am I? Let’s say I’m here You’re here (origin)
I call you on the cell phone. How do I tell you how to get to me?
2 equivalent ways:
Travel 11.2 km at an angle of 26.5 degrees
Travel 10 km East then 5 km North
My single vector in some funny direction, can be thought of as two vectors in nice simple directions (like X and Y). This can make things much easier
Physics 218, Lecture II

16. Adding vectors is a skill Use this in far more than just physics
Vector Addition
To specify where I am, often doing the two vector version is easier
Represent Graphically:
Lay down first vector
Lay down second vector
Put the tail at the head of the first vector
The “Sum” is where I am
Adding vectors is a skill
Use this in far more than just physics
More on this later…
Physics 218, Lecture II

17. Re-write my location
Describe my location in terms of the sum of two vectors
Careful when using the sin and cos
Physics 218, Lecture II

18. Specifying a Vector
Two equivalent ways:
Components Vx and Vy
Magnitude V and angle q
Switch back and forth
Magnitude of V
|V| = (vx2 + vy2)½ Pythagorean Theorem
Tanq = vy /vx
Either method is fine, but you should pick which is easiest, and be able to use both
Physics 218, Lecture II

19. Unit Vectors This is how the pros write things!
Physics 218, Lecture II

20. Unit Vectors
The pros also use:
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21. Vector in Unit Vector Notation
Physics 218, Lecture II

22. General Addition Example
Add two vectors using the i-hats, j-hats and k-hats
Physics 218, Lecture II

23. How do we Multiply Vectors?
First way: Scalar Product or Dot Product
Why Scalar Product?
Because the result is a scalar (just a number)
Why a Dot Product?
Because we use the notation A.B
A.B = |A||B|CosQ
Physics 218, Lecture II

24. First Question:
A.B = |A||B|CosQ
Physics 218, Lecture II

25. Harder Example
Physics 218, Lecture II

26. Vector Cross Product
This is the last way of multiplying vectors we will see
Direction from the “right-hand rule”
Swing from A into B!
Physics 218, Lecture II

27. Vector Cross Product Cont…
Multiply out, but use the Sinq to give the magnitude, and RHR to give the direction
Physics 218, Lecture II

28. Cross Product Example
Physics 218, Lecture II

29. Results of Math Quizzes
The average of all Math Quizzes taken so far (not the Math Assessment) is about an 8.1 with a standard deviation of just above 1.1.
How to evaluate where you stand. If the average of the scores of all the quizzes you have taken is:
95% or above: Well prepared
85% - 90%: Good, but needs to be better
80% – 85%: Ok, but really needs some work
75% - 80%: Hmmmm…maybe get some help
75% or below: Careful…Definitely get help! Maybe drop…
Physics 218, Lecture II

30. For Next Week Before Lecture: Read Chapter 2 Math Quizzes due Monday
Lecture Assignment: Q2.8 and Q2.20 (These are the “Discussion Questions”)
In Lecture
Cover Chapter 2
Turn in Lecture Assignment at the beginning
Recitation, Lab and Homework:
Start HW1 on WebCT before recitation
All Ch. 1 problems due Monday after recitation
Read your lab materials before lab
Physics 218, Lecture II

31. End of Lecture Notes
Physics 218, Lecture II

32. Simple Multiplication
Multiplication of a vector by a scalar
Let’s say I travel 1 km east. What if I had gone 4 times as far in the same direction?
→Just stretch it out, multiply the magnitudes
Negatives:
Multiplying by a negative number turns the vector around
Physics 218, Lecture II

33. Subtraction Subtraction is easy:
It’s the same as addition but turning around one of the vectors. I.e., making a negative vector is the equivalent of making the head the tail and vice versa. Then add:
Physics 218, Lecture II

34. Where am I?
Traveling East then North is the same as traveling NorthEast
Can think of this the other way: If I had gone NorthEast, the displacement is equivalent to having gone both North and East
My single vector in some funny direction, can be thought of as two vectors in nice simple directions (like X and Y). This can make things much easier
Physics 218, Lecture II

35. Problem Solving & Diagrams
This class is mostly problem solving (well… you need to understand the concepts first in order to solve the problems, but we’ll do both).
In order to solve almost any problem you need a model
Physicists/engineers are famous for coming up with silly models for complicated problems
The first step is always:
Trick #2:“Draw a diagram!”
Physics 218, Lecture II

36. Announcement: Free Tutoring
Four foreign graduate students are available to tutor Physics 218 Students without charge. Students desiring help are to the tutor and arrange a time to meet in Heldenfels 211 on weekdays. The tutors are:
Sunnam Min,
Xi Wang,
Rongguang Xu,
Hong Lu,
Physics 218, Lecture II

37. Components Let’s do this with the math:
Break a vector into x and y components (I.e., a right triangle) THEN add them
This is the sine and cosine game
Can use the Pythagorean Theorem A2 + B2 = C2
Physics 218, Lecture II

38. Chapter 1: Introduction
This chapter is fairly well written. I won’t lecture on most of it except for the parts which I think are useful in helping you be a better problem solver in general or at least helping you look like a professional
Physics 218, Lecture II

39. Models, theories and Laws
Prescriptive vs. Descriptive
What should happen vs. What does happen when you do an experiment
US law doesn’t allow killing
Physics law shows clearly that it does happen.
Physics 218, Lecture II

40. Estimating Order of Magnitude
This is a useful thing to be able to do at home
Let’s say you are at a grocery store and it’s full. How much will it cost you to buy it all?
Estimate using round numbers
50 items (assuming not lots of little things)
A dollar an item
 $50
Physics 218, Lecture II

41. Number of Significant Figures
15 ± 1 feet (1 digit in uncertainty, same “10’s” as last digit)
± 1 feet (Makes you look like an amateur)
15 ± 1.05 feet (Same thing)
15.1 ± 0.1 feet (Ok)
15 ± 10 feet (Ok)
An aside: Personally, I take significant digits seriously. It makes you look bad when you mess them up. Also, WebCT will do unpredectible things if you don’t use them correctly.
Physics 218, Lecture II

42. Converting Units 1 meter x 1 = 1 meter
Multiplying anything by 1 (no units!) is a GREAT trick! Use it often!!
1 meter x 1 = 1 meter
1 yard x 1 = 1 yard x (3 feet/yard) = 3 feet (simple! Units cancel out!)
Example:1 football field in feet
1 football field x (1) x (1) = 1 football field
1 football field x (100 yards/1 football field) x (3 feet/yard) = 300 feet
Both are units of length!
Physics 218, Lecture II

43. Significant Figures
Good test: Write the primary number as 1.5x101 feet (get rid of zeros on either end) which is the “powers of 10 notation” or what we call “scientific notation”
= x 104
Then deal with the uncertainty
Usually only one digit in the uncertainty
Example: Fix ± 1 feet
→ ( ± 0.1) x 101 feet
→ (1.5 ± 0.1) x 101 feet
Physics 218, Lecture II

44. Reference Frames Need to refer to some place as the origin
Frame of reference:
Need to refer to some place as the origin
Draw a coordinate axis
We define everything from here
Always draw a diagram!!!
Physics 218, Lecture II

45. First the Math: Vector Notation
In the book, variables which are vectors are in bold
On the overheads, I’ll use an arrow over it
Vectors are REALLY important
Kinda like calculus: These are the tools!
Some motion represented by vectors. What do these vectors represent physically?
Physics 218, Lecture II

46. Adding vectors in funny directions
Let’s say I walk in some random direction, then in another different direction. How do I find my total displacement?
We can draw it
It would be good to have a better way…
Physics 218, Lecture II

47. Example
We have two known displacements D1 and D2. What is the magnitude and angle of the net displacement in this example?
Physics 218, Lecture II

48. Go home with a friend
You are going home with a friend. You live in Houston and your friend lives in San Antonio. First you drive 100 miles SouthEast (known angle Q) from Aggieland to Houston, then 300 miles West to San Antonio? Using unit vector notation, what is your displacement from the center of the universe?
Physics 218, Lecture II

49. Examples without an axis
Physics 218, Lecture II

50. Addition using Components
To add two vectors, break both up into their X and Y components…
First break each vector into its X and Y components
Physics 218, Lecture II

51. Addition using Components cont…
Next: add separately in the X and Y directions
Magnitudes
of VF
Physics 218, Lecture II

52. Drawing the components
Physics 218, Lecture II

53. Vector Cross Product Cont…
Calculating the cross product is the same as taking the determinant of a Matrix
Physics 218, Lecture II