Looking Back What is a motion diagram What is particle model What are basic elements of a coordinate system Distance and displacement 1 Looking Back A motion diagram is a composition image showing an object s position at several equally spaced instants of time In Particle model the object is treated as if all its mass were concentrated at a single point called a particle Position where the location of the object A coordinate system contains an origin point axes with scale direction and unit x m 100 50 0 50 100 150 One dimensional coordinate system using an x axis origin scale units 2 Distance Displacement Speed and Velocity Distance is actual length of an object traveled regardless of its direction A scalar Displacement is a change of position including the direction of motion A vector x xf xi 3 Answer to Checking Understanding 1 Alice is sliding along a smooth icy road on her sled when she suddenly runs headfirst into a large very soft snowbank that gradually brings her to a halt Draw a motion diagram for Alice Show and label all displacement vectors 2 Maria is at position x 23 m She then undergoes a displacement x 50 m What is her final position A 27 m B 50 m C 23 m D 73 m 50m x f 23m x f 23m 50m 27 m 4 In Brief Physical quantities Position Distance Displacement Speed Velocity Goals for today Scalars and vectors A sense of scale Significant figures Scientific notation SI Units Definition notation and application Before next Tuesday Review Ch 1 Quiz 1 next Tuesday Read Chapter 2 sections 1 3 Student Workbook Ch 1 problems 19 22 MP HW 2 Math Review available tomorrow 5 Distance Displacement Speed and Velocity Distance is actual length of an object traveled regardless of its direction Scalar Displacement is a change of position including the direction of motion Vector distance traveled in a given time interval speed time interval displaceme nt x velocity time interval t 1 1 1 2 A change in any quantity is the final value of the quantity minus its initial value 6 Speed a scalar Motion diagrams for a car and a bicycle m The car moves 40 m in 1 s The bike moves 20 m in 1 s 40 m Its speed is 1s 20 m Its speed is 1s 40 m s m 20 s 7 Velocity a vector Motion diagrams for two bicycles 40m 20m 2s 1s 20m s Bike1 60m 100m 3s 1s 20m s Bike2 m Two bicycles traveling at the same speed but with different velocities An object s velocity vector points in the same direction as its displacement vector 8 Questions 1 How much distance did you travel to school today and in how much time What was your average speed 2 You go from home to school and then back home in the evening What total distance did you travel What is your net displacement What is the velocity of a round trip 9 Scalars and vectors Scalar quantities can be expressed by a single number with a unit Time distance speed temperature are scalars A scalar can be positive negative or zero Vector quantities need both a magnitude and direction Displacement velocity acceleration force are vectors The magnitude of a vector can be positive and zero not negative Notation A magnitude length Direction 10 Vectors A A Are these vectors equal or different B B C These vectors are equal A B C C These vectors are different 11 Vectors A displacement vector drawn from the initial to the final position pointing the final position A B The displacement vector of a car initial point A final point B Regardless of the actual path 12 Vectors A velocity vector pointing the direction of the motion A B 13 Vectors In motion diagrams Displacement Vectors Velocity Vectors 14 Example Velocity Vectors Jake throws a ball at a 60 angle measured from the horizontal The ball is caught by Jim Draw a motion diagram of the ball with velocity vectors 15 Vector Addition Example of sum of two vectors Sam undergoes two displacements 16 Vectors Sum of two vectors Adding Vectors Graphically 17 Example Adding Displacement Vectors Jenny runs 1 mi to the northeast then 1 mi south Graphically find her net displacement 18 Vectors A vector can be decomposed into its components A two dimensional coordinate system A Ax Ay y A o Ax Ay x How to compute lengths magnitude and angles direction of triangles Need trigonometry 19 Vectors and Trigonometry O sin H cos A H tan Also review Pythagorean theorem O A H 2 A2 O 2 20 Vectors and Trigonometry sin O H O tan A y A o Ax sin Ay x tan Ay A Ay Ax cos A H H 2 A2 O 2 Ax cos A A2 Ax2 Ay2 21 Stop to think 1 5 P and Q are two vectors of equal length but different direction Which vector shows the sum of P Q 22 Take home quiz due next Tuesday Jan 21 from Student Workbook 1 14 1 17 st Refer to section 4 in Ch 1 A sense of scale 1 How many significant figures does each of the following numbers have a 6 21 c 6210 0 e 6 21x103 b 0 0621 d 1 0621 f 6 21x10 3 2 Compute the following numbers applying the significant figure standards adopted for this text c 33 3x25 4 b 33 3 25 4 C 4 32x1 23 5 1 3 Express the following numbers and computed results in scientific notation paying attention to significant figures d 9 827 b 0 000000550 c 3 200 000 4 Convert the following to SI units a 9 12 s b 3 42km c 80km hr Student Workbook problems Chapter 1 1 3 6 8 10 and 12 19 22 New Reminder Take Home Quiz due next Tuesday 24