Physics 218 Summer 2009 Deepak K Pandey Office:Physics 87 Phone:

Today: (Ch. 1 & 2)  Motion, Forces and Newton’s law  Graphs Tomorrow: (Ch. 2 & 3)  Force and Motion Along a Line HDisplacement, Velocity and Acceleration HNormal force and weight HFriction

Chapter 2: Motion, Forces and Newton’s law Scalars and Vectors Forces Newton’s law of motion Net force (vector addition) Free body diagram Contact forces (tomorrow)

Scalars and Vectors Vocabulary: Scalars are numbers Examples: 10 meters 75 kilometers/hour Vectors are numbers with a direction Example: 10 meters to the right 75 kilometers/hour north

Scalars and Vectors Scalar: 25 meters Vector: 25 meters north Scalar: 25 meters Vector: 25 meters east

Adding Vectors To add two vectors, A + B A B 1. place the head of one vector on the tail of the other vector B A 2. draw a new vector from the tail of the first to the head of the second B AC 3. This new vector is is called the resultant A + B = C

Subtracting Vectors To subtract two vectors, A - B A B 1. Multiply vector B by -1: A + (-B) A -B 2. Then simply add A and -B, head to tail. -B A C 3. A + -B = C

The Components of a Vector A = x + y We call x and y the components of the vector A. A y x O P

Addition of Vectors (using Components) A + B = C Add the x components of A and B to each other to get the x component of C. Then, add the y components of A and B to each other to get the y component of C. Let see How do we find the x and y components? C B A

Addition of Vectors (using Components) A A x A y B x B y B C C x C y

Example If B has a magnitude of 25 kilometers in a direction 30 degrees North of East, what is the x component of B? B B y B x  =30 o

Example You travel 2 km due East on 26th street, then turn right on Main street and head Southeast for 1 km, what are the components of your displacement?

Group Problem Solving If A has a magnitude of 10 meters, and is pointing 45 degrees South of East, what is the magnitude (length) of the vector A y ? AyAy A  AxAx

x0x0 Net Force: Vector addition

x  vector to final position x

  change in  x  displacement (change in position)  x = x - x 0 xx Displacement

  change in  x  displacement (change in position)  x = x - x 0 xx Displacement x  vector to final position x x 0  vector to initial position x0x0

Speed and Velocity Speed is a scalar: what your speedometer reads. (meters/second) Velocity is a vector: the speed, in a certain direction (meters/second at  degrees) Examples: 100 meters/second 41 kilometers/hour Southwest

Average Speed & Velocity average velocity = average speed in the specified direction

Average Acceleration

Example A police airplane notices that your car only took 2 seconds to travel between two white marks on the highway that are 100 meters apart. Will you get a ticket?

Graphical Representation

Example: Ball rolling up and down

HW1: Dimensional Analysis Consider the equation mgh = mv 2, where m has dimensions of mass (units of kilograms), g has dimensions of length/time 2 (m/s 2 ), h has dimensions of length (meters), and v has units of length/time (m/s). a.Is this equation dimensionally correct or incorrect? b.What is the units of the combination g/v 2 ?

HW1: Density The mass of an object is m = 26 kg, and its volume is V = m 3. What is its density, m/V? Be sure to give the correct number of significant figures in your answer. Number of significant digits required = 1

Tomorrow: (Ch. 2 & 3)  Force and Motion Alone a Line  Displacement, Velocity and Acceleration

Addition of Vectors (using Components) A A x A y B x B y C B C x C y