TUTOR & HOMEWORK SESSIONS for Physics 113 This year’s tutors: Chad McKell, Xinyi Guo

 

All sessions will be in room Olin 103

 Tutor sessions in past semesters were very successful and received high marks from students.

All students are encouraged to take advantage of this opportunity. 

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

4-6 pm

Chad McKell

5-7 pm

Chad McKell

5:15 – 7:15 pm

Xinyi Guo

4-6 pm

Chad McKell

Announcements:

• Read preface of book for great hints on how to use the book to your best advantage!!

• Labs begin Jan. 29 (buy lab manual).

• Bring ThinkPads to first lab (and some subsequent labs)!

• Questions about WebAssign and class web page?

• My office hours: MTWHF 1:00 pm - 2:00 pm, Olin 302.

• Pay attention to demos (may pop up in exams).

• Keep homework work sheets, etc (to prepare for exams).

• Keep a good, well-organized notebook (ppt slides, notes, homework)

• In this chapter we will learn about vectors.

properties, addition, components of vectors

• When you see a vector, think components!

• Multiplication of vectors will come in later chapters.

• Vectors have magnitude and direction.

Chapter 3: VectorsReading assignment: Current: Chapter 3

Homework: CQ1, CQ2, 3, 7, 11, 13, 18, 19, 24, 29, 30, 32, 41, AE1, AE4, AE5

Due dates: Tu/Th section: Monday, Jan. 31

MWF section: Wednesday, Feb. 2

CQ – Conceptual question, AF – active figure, AE – active example

No need to turn in paper homework for problems that mention it. Remember: Homework 2 is due Wednesday, Jan. 25 (section B), Jan. 27 (section A).

Vectors: Magnitude and direction

Scalars: Only Magnitude A scalar quantity has a single value with an appropriate unit and has no direction.

Examples for each:

Vectors:

Scalars:

Motion of a particle from A to B along an arbitrary path (dotted line). Displacement is a vector

Coordinate systems

Cartesian coordinates:

abscissa

ordinate

Vectors:

• Represented by arrows (example: displacement).

• Tip points away from the starting point.

• Length of the arrow represents the magnitude.

• In text: a vector is often represented in bold face (A) or by an arrow over the letter; .

• In text: Magnitude is written as A or A

A

This four vectors are equal because they have the same magnitude (length) and the same direction

Adding vectors:

Draw vector A.

Draw vector B starting at the tip of vector A.

The resultant vector R = A + B is drawn from the tail of A to the tip of B.

Graphical method (triangle method):

Example on blackboard:

Adding several vectors together. Resultant vector

R=A+B+C+D

is drawn from the tail of the first vector to the tip of the last vector.

Example on blackboard:

A + B = B + A(Parallelogram rule of addition)

Commutative Law of vector addition

Order does not matter for additions

Example on blackboard:

Associative Law of vector addition

A+(B+C) = (A+B)+CThe order in which vectors are added together does not matter.

Example on blackboard:

Negative of a vector.The vectors A and –A have the same magnitude but opposite directions.

A + (-A) = 0

A -A

Subtracting vectors:

A - B = A + (-B) Example on blackboard:

Multiplying a vector by a scalar

The product mA is a vector that has the same direction as A and magnitude mA (same direction, m times longer).

The product –mA is a vector that has the opposite direction of A and magnitude mA.

Examples: 5A; -1/3A

Components of a vector

sin

cos

AA

AA

y

x

22yx AAA

x

y

A

A1tan

The x- and y-components of a vector:

The magnitude of a vector:

The angle q between vector and x-axis:

Example on blackboard:

A

i-clicker:

You walk diagonally from one corner of a room with sides of 3 m and 4 m to the other corner. What is the magnitude of your displacement (length of the vector)?

A. 3 mB. 4 mC. 5 mD. 7 mE. 12 m

A

The signs of the components Ax and Ay depend on the angle q and they can be positive or negative.

(Examples)

Unit vectors• A unit vector is a dimensionless vector having a magnitude 1.• Unit vectors are used to indicate a direction. • i, j, k represent unit vectors along the x-, y- and z- direction• i, j, k form a right-handed coordinate system

Right-handed coordinate system:

Use your right hand:

x – thumb x – index

y – index finger or: y – middle finger

z – middle finger z – thumb

Which of the following coordinate systems is not a right-handed coordinate system?

x

xx

y

y

yz

z

z

A B C

The unit vector notation for the vector A is:

A = Axi + Ayj

The column notation often used in this class:

y

x

A

AA

Vector addition using unit vectors:

We want to calculate: R = A + B

From diagram: R = (Ax + Bx)i + (Ay + By)j

The components of R: Rx = Ax + Bx

Ry = Ay + By

Only add components!!!!!

2222 )()( yyxxyx BABARRR

xx

yy

x

y

BA

BA

R

Rtan

The magnitude of a R:

The angle q between vector R and x-axis:

Vector addition using unit vectors:

Blackboard example 3.1

A commuter airplane takes the route shown in the figure. First, it flies from the origin to city A, located 175 km in a direction 30° north of east. Next, it flies 153 km 20° west of north to city B. Finally, it flies 195 km due west to city C

(a) Find the location of city C relative to the origin (the x- and y-components, magnitude and direction (angle) of R.

(b) The pilot is heading straight back to the origin. What are the coordinates of this vector.

Polar Coordinates

A point in a plane: Instead of x and y coordinates a point in a plane can be represented by its polar coordinates r and q.

sin

cos

ry

rx

x

ytan 22 yxr

Blackboard example 3.2

A vector and a vector are given in

Cartesian coordinates.

(a) Calculate the vector .

(b) What is the magnitude of ?

(c) Find the polar coordinates of .

4

3A

2

3B

BAC

43

C

C