Physics 218 Lecture 5 Dr David Toback Physics

Physics 218 Lecture 5 Dr. David Toback Physics 218, Lecture V 1

Notes • Updated Class Schedule on my web page – New lab assignments/dates – New reading/chapter assignments (i. e. , what we are doing each week) • End of Chapter quizzes coming soon. Will let you know when they are posted Physics 218, Lecture V 2

Checklist for Today • Things that were due last Thursday: – Chapter 2 reading – Read all handouts from web page • Things that are due yesterday (Monday): – Web. CT Prelim (FCI, Math Assess, etc…) – Math Quizzes 1 through 10 • Things that are due today: – Reading for Chapters 3 & 4 • For this week and/or due next Monday: – Recitation: Start Ch. 2 on Web. CT – All HW 2 problems on Web. CT due Monday Physics 218, Lecture V 3

This Week Chapters 3 and 4 – Vectors and Two Dimensional Motion – Do these two chapters together • Vectors • Position, Velocity and Acceleration • Projectile Motion Physics 218, Lecture V 4

Physics 218, Lecture V 5

Physics 218, Lecture V 6

Vectors • Why we care about them • Addition & Subtraction Physics 218, Lecture V 7

Why do we care about Vectors? As you may have noticed, the world is not one-dimensional • Three dimensions: X, Y and Z. • Example: 1. Up from us 2. Straight in front of us 3. 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 V 8

Vector and Scalar • Vectors have a magnitude AND a direction – I’m driving 70 miles/hr South. East to Houston • Scalars are just a number – My speedometer says 70 m/hr Physics 218, Lecture V 9

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: My single vector in some 1)Travel 11. 2 km at an funny direction, can be angle of 26. 5 degrees thought of as two vectors 2)Travel 10 km East in nice simple directions then 5 km North (like X and Y). This can make things much easier 10 Physics 218, Lecture V

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 V 11

Specifying a Vector • Two equivalent ways: – Components Vx and Vy – Magnitude V and angle q • Switch back and forth – Magnitude of V |V| = (vx 2 + vy 2)½ Pythagorean Theorem – Tanq = vy /vx Either method is fine, but you should pick which is easiest, and Physics 218, Lecture V be able to use both 12

Unit Vectors This is how the pros write things! Physics 218, Lecture V 13

Unit Vectors The pros also use: Physics 218, Lecture V 14

Vector in Unit Vector Notation Physics 218, Lecture V 15

General Addition Example Add two vectors using the ihats and jhats Physics 218, Lecture V 16

Motion in 2 -Dimensions • Moving from Chapter 3 to Chapter 4 • This is what all the setup has been for! • Motion in two and three dimensions – For now we’ll ignore air friction Physics 218, Lecture V 17

Position in 2 dimensions Physics 218, Lecture V 18

Velocity in 2 dimensions Physics 218, Lecture V 19

Acceleration in 2 dimensions Physics 218, Lecture V 20

Projectile Motion The physics of the universe: The horizontal and vertical Equations of Motion behave independently This is why we use vectors in the first place Physics 218, Lecture V 21

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 V 22

How to Solve Problems The trick for all these problems is to break them up into the X and Y directions Physics 218, Lecture V 23

Ball Dropping Analyze Vertical and Horizontal separately!!! • Ay = g (downwards) • Ax = 0 – Constant for Both cases!!! Vx = 0 Vx>0 Physics 218, Lecture V 24

A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically Physics 218, Lecture V 25

Firing up in the air at an angle A ball is fired up in the air with speed Vo and angle Qo. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here? Physics 218, Lecture V 26

Next time… • Reading: None, you’ve already finished Chapter 3 & 4 already • Homework: – HW 1 was due yesterday – HW 2 covered in recitation this week; due this coming Monday – Start working on HW for Chap 3 & 4 • Next time: More on kinematics in two dimensions Physics 218, Lecture V 27

Physics 218, Lecture V 28

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 Adding vectors is a skill vector Use this in far more • The “Sum” is where I than just physics am More on this later… Physics 218, Lecture V 29

Vectors: –Why we care about them –Addition & Subtraction –Unit Vectors –Multiplication Physics 218, Lecture V 30

Position in 3 dimensions Physics 218, Lecture V 31

General Addition Example Add two vectors using the ihats, j-hats and k-hats Physics 218, Lecture V 32

Velocity in 3 dimensions Physics 218, Lecture V 33

A Mail Carrier A rural mail carrier leaves the post office and drives D 1 miles in a Northerly direction to the next town. She then drives in a direction q degrees South of East for a distance D 2 to another town. What is the magnitude and angle of her displacement from the Physics 218, Lecture V 34

Constant Acceleration Physics 218, Lecture V 35

Example: Adding Unit Vectors Physics 218, Lecture V 36

Vector stuff 1. Pythagorean theorem: We’ll use this a lot – – – For a right triangle (90 degrees) Length C is the hypotenuse A 2 + B 2 = C 2 2. Vector equations Physics 218, Lecture V 37

Using all this stuff Physics 218, Lecture V 38

Unit Vectors This is how the pros write things! Physics 218, Lecture V 39

Unit Vectors The pros also use: Physics 218, Lecture V 40