Lecture 2: Physics 103

1. Lecture 2: Physics 103 • Measurement • Problem solving • Kinematics Physics 103, Fall 2009, U.Wisconsin

2. Physics 103 • Consult the course web site, especially the planner http://tycho.physics.wisc.edu/courses/phys103/fall09 • Should be • Reading chapter before class • Doing pre-flights - one for today on physics was due at noon • There are pre-flights for every lecture • Going to discussion section and lab • Pre-lab questions for your first lab next week (TA will email) • Homework, due Friday at noon, 80% credit if late by less than 1 week • Quiz due Sunday at noon. Can take quiz starting Thursday at 6PM. (take it early!) • Try practice exams when exam time comes Physics 103, Fall 2009, U.Wisconsin

3. Course Outline • Mechanics • kinematics • energy • momentum • rotational motion • gravity • Solids & Fluids • Heat • Waves Rockets and Satellites: Satellite TV, GPS, Maps Effective water distribution better understanding of the heart and blood flow Energy efficient air-conditioning, heat Understanding of light waves: Radio, TV, Cell phones, microwave ovens Physics 103, Fall 2009, U.Wisconsin

4. Units • To communicate the result of a measurement for a quantity, a unit must be defined • Defining units allows everyone to relate to the same fundamental amount • Length [L]: meters • Mass [M]: kilograms • Time [T]: seconds • Dimensional Analysis: • Both sides of an equation must have the same dimensions • Can be used to verify equations, answers Physics 103, Fall 2009, U.Wisconsin

5. A Concept • All of these quantities have units • Distance: measured in meters, miles, feet … • Time: measured in seconds, hours, years … • Speed: meters per second, miles per hour … • Fundamental units • Derived units • Speed: meters per second (m/s), miles per hour (mph) Physics 103, Fall 2009, U.Wisconsin

6. Significant Figures • There is uncertainty in every measurement, this uncertainty carries over through the calculations • Use rules for significant figures to approximate the uncertainty in results of calculations • A significant figure is one that is reliably known • All non-zero digits are significant • Zeros are significant when • between other non-zero digits • After the decimal point and another significant figure • can be clarified by using scientific notation • Significant figures in a final result equals significant figures in the least accurate of the factors being combined • Hint: Keep at least one more significant figure in your calculation than needed until the very end, then round your final answer (I keep 2 to be safe!) Physics 103, Fall 2009, U.Wisconsin

7. Significant Figure Example • You are asked to calculate a trajectory for a space ship to the moon to 1% accuracy. • If your off by more than 1% you might miss the moon and not have enough fuel to correct course and land! • 1% is the accuracy we ask for in the homework questions • Formula: distance = 1/2 acceleration*time2: x = 1/2at2 • Steps. Find “a” given you have to arrive at a certain time. Confirm the ship covers the distance and arrives at the right place! • x = 3.8440x108 m, t = 10049 sec: a = 7.6132 m/s2, • Known to 1% precision: 1 part in 100 or 3 decimal places • Case 1: After figuring out t and a we round off to 1% precision: x = 1/2at2 = 1/2*100002*7.6 = 380,000,000m • Case 2: We keep 5 significant figures to be safe: x = 1/2at2 = 1/2*10049*7.6132 = 384,400,000m • In case 1 we are 1.1% off. You just killed the astronauts! • Lesson: to get 1% accuracy keep 5 digits and round at end Physics 103, Fall 2009, U.Wisconsin

8. Order of Magnitude Estimates correct A very good fastball pitcher can throw the ball 100 mph. What is the ball speed in m/s? (5 miles is approximately 8 km) • 4444 m/s • 44.44 m/s • .4444 m/s Order of magnitude estimate: A mile is of order 103 meters An hour is of order 103 seconds Therefore, the answer should be of order 102 m/s Physics 103, Fall 2009, U.Wisconsin

9. Problem Solving: Diagrams Physics 103, Fall 2009, U.Wisconsin

10. Lightning Question burst Lightning was observed and thunder followed 5.0s later - Given speed at which light (c=3.0x108 m/s) and sound (v=3.3x102 m/s) travel, can we calculate how far away the “cloud burst” was? 1. Yes 2. No Distance x Label all quantities: Distance of cloud burst - x Time of cloud burst - t0 Time lightning seen - tL Time thunder heard - tS Write relations: Solve: 3 equations but 4 unknowns. Surprise: In this case the solution is possible! Physics 103, Fall 2009, U.Wisconsin

11. Solution to Lightning Question Physics 103, Fall 2009, U.Wisconsin

12. Lightning Question Lightning was observed and thunder followed 5.0s later - Given speed at which light (c=3.0x108 m/s) and sound (v=3.3x102 m/s) travel, can we calculate how far away the “cloud burst” was? Neglecting time taken for light to travel - since it travels so fast, what is the distance of cloud burst from the observer? 1. 17 km 2. 1.7 km 2 significant figures Physics 103, Fall 2009, U.Wisconsin

13. Units, Significant Figures, Estimates • Fundamental Units • Length [L]: meters • Mass [M]: kilograms • Time [T]: seconds • Dimensional Analysis: • Both sides of an equation must have the same dimensions • Can be used to verify equations, answers: v=d/t, m/s = m/s • Significant Figures: • Final significant figures determined by number with the least significant figures used in the calculation • Keep at least two extra digits along the way and round at the end(5 for 1% accuracy) • Order of magnitude estimates also useful to double check answers Physics 103, Fall 2009, U.Wisconsin

14. Problem Solving Lightning was observed and thunder followed 5.0s later - Given speed at which light (c=3.0x108 m/s) and sound (v=3.3x102 m/s) travel, can we calculate how far away the “cloud burst” was? Draw a picture Write down all the things you know Write down relevant equations Try to simplify if possible Check answer with dimensional analysis and order of magnitude estimates Round to significant figures 1.7 km Physics 103, Fall 2009, U.Wisconsin

15. Kinematics • Kinematics: Let’s you track position of an object? • Where is it? How fast is it moving? Which direction? How fast is its speed changing? - Where will it be in future? • We will be tracking the position of a point • When a ball moves, it is the center of the ball that we describe. • More on center of mass later in the semester. Coordinate Systems: Physics 103, Fall 2009, U.Wisconsin

16. Position and Displacement • Position: xi -- defined in terms of a frame of reference (location of origin) • Displacement: Dx = xf - xi (i stands for initial, f for final) • Movement in one dimension: label axis as x -- horizontal (y for vertical) • Can be positive or negative - i.e., it has direction • Object can move towards right or left of position x=0 • Units are meters Physics 103, Fall 2009, U.Wisconsin

17. Kinematics: Distance and total distance • Distance: the magnitude or size of displacement • Has no direction : absolute value : |xf - xi| • I displace myself (from origin) -3 m and then +1m • My displacement (from origin) is -2 m • My distance (from origin) is 2 m • Total distance I moved is could be 4 m • Not very useful to determine where I am • Useful for determining how many frequent flyer miles are awarded after a round-trip flight. Physics 103, Fall 2009, U.Wisconsin

18. Question ? An object goes from one point in space to another. After it arrives at its destination, itsdisplacementis: • either greater than or equal to • always equal to • either less than or equal to • not related to thedistanceit traveled. Displacement can be negative, and when it is, it is less than distance, which is the absolute value of displacement! The distance and displacement of an object is not the same as the total distance it travels: The total distance is always going to be the longest Throw a ball straight up and catch it at the same point you released it: The total distance is twice the height, but the displacement is zero! Physics 103, Fall 2009, U.Wisconsin

19. Speed • The average speed of an object is defined as the total distance traveled divided by the total time elapsed • Average speed totally ignores any variations in the object’s actual motion during the trip • The total distance and the total time are all that count • Units are meters/second s Physics 103, Fall 2009, U.Wisconsin

20. Average Velocity • Average velocity is the displacement divided by the time interval and has the same direction as displacement Units are meters/second • Velocity has direction (can be positive or negative when motion is in one dimension) • Speed is not velocity: car on straight highway vs. car on winding country road take same time between 2 towns • Average velocity same • Average speed (country rd) > average speed (highway) • Highway had traffic jam! Physics 103, Fall 2009, U.Wisconsin

21. Instantaneous Velocity • Instantaneous velocity is the average velocity over an infinitesimal (very short) time interval. • Instantaneous velocity applies to one point of time. • Example: drive slowly, then speed up to pass a car. • Special Case: Uniform velocity is constant velocity • Instantaneous velocities are always the same • Instantaneous velocities also equal the average velocity Physics 103, Fall 2009, U.Wisconsin

22. Average Velocity • Position vs. time graph • Motion is non-constant velocity • Average velocity is the slope of blue line joining two points 20 m/s 13.33 m/s 20 m/s 0 m/s -6 m/s Average is not necessarily speed at which object is moving at any instance! Physics 103, Fall 2009, U.Wisconsin

23. Instantaneous Velocity Instantaneous velocity is slope of tangent at any point and applies to that point in time only Physics 103, Fall 2009, U.Wisconsin