1. Free Fall Introduction Section 0 Lecture 1 Slide 1 Lecture 5 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall

2. Introduction Section 0 Lecture 1 Slide 2 Lecture 5 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Free Fall Introduction Section 0 Lecture 1 Slide 3 Lecture 5 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall Introduction

4. Free Fall Introduction Section 0 Lecture 1 Slide 4 Lecture 5 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 More Than Just A Cool Name Galileo Galilei ranks 12 th on Hart’s list of most influential people in the history of the world behind Newton (2) and Einstein (10). Galileo ranks 7 th on Simmon’s list of most influential scientists in the history of the world ( behind Newton, Einstein, Bohr, and just ahead of Kepler, Copernicus, Farady and Maxwell.

5. Free Fall Introduction Section 0 Lecture 1 Slide 5 Lecture 5 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Describing (Special) Motion Position—where you are in space (L-meter) Speed—how fast position is changing with time (LT -1 or m/s) Acceleration—how fast speed is changing with time (LT -2 or m/s 2 ) We will focus on a special case of constant acceleration due to gravity, termed FREE FALL.

6. Free Fall Introduction Section 0 Lecture 1 Slide 6 Lecture 5 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Acceleration Acceleration is the rate at which velocity changes. –Our bodies don’t feel velocity, if the velocity is constant. –Our bodies feel acceleration. A car changing speed or direction. An elevator speeding up or slowing down. Acceleration can be either a change in the object’s speed or direction of motion. t 1 VV intervalTime velocityinChange accelerationAverage 2    2 sm t V a     In this Chapter acceleration is a constant, a=g=9.8 m/s 2

7. Free Fall Introduction Section 0 Lecture 1 Slide 7 Lecture 5 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall Influence of Gravity

8. Free Fall Introduction Section 0 Lecture 1 Slide 8 Lecture 5 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 State of Physics cira 1895 Conservation Laws Energy Linear & Angular Momentum Statistical Mechanics 3 Laws of Thermodynamics Kinetic Theory

9. Free Fall Introduction Section 0 Lecture 1 Slide 9 Lecture 5 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How does a dropped object behave?  Does the object accelerate, or is the speed constant?  Do two objects behave differently if they have:  different masses?  different shapes?

10. Free Fall Introduction Section 0 Lecture 1 Slide 10 Lecture 5 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Acceleration Due to Gravity Earth exerts a gravitational force on objects that is attractive (towards Earth’s surface). Near Earth’s surface, this force produces a constant acceleration downward. –To measure this acceleration, we need to slow down the action. –Galileo was the first to accurately measure this acceleration due to gravity. –By rolling objects down an inclined plane, he slowed the motion enough to establish that the gravitational acceleration is uniform, or constant with time.

11. Free Fall Introduction Section 0 Lecture 1 Slide 11 Lecture 5 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Inclined Plane Experiment  Does the marble pick up speed as it rolls?  Is it moving faster at the bottom of the incline than it was halfway down?

12. Free Fall Introduction Section 0 Lecture 1 Slide 12 Lecture 5 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall An Object In Free Fall

13. Free Fall Introduction Section 0 Lecture 1 Slide 13 Lecture 5 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Flashes of a stroboscope illuminate a falling ball at equal time intervals. Distance covered in successive time intervals increases regularly. Since distance covered in equal time intervals is increasing, the velocity must be increasing. An Object In Free Fall

14. Free Fall Introduction Section 0 Lecture 1 Slide 14 Lecture 5 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Average velocity for a time interval is given by dividing the distance traveled in that time interval by the time of the interval. For example, between the 2 nd and 3 rd flashes, the ball travels a distance of 4.8 cm - 1.2 cm = 3.6 cm in a time of 0.05 s: An Object In Free Fall

15. Free Fall Introduction Section 0 Lecture 1 Slide 15 Lecture 5 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The velocity values steadily increase. TimePositionAverage velocity 0 s0 cm 0.05 s1.2 cm24 cm/s 0.10 s4.8 cm72 cm/s 0.15 s11.0 cm124 cm/s 0.20 s19.7 cm174 cm/s 0.25 s30.6 cm218 cm/s 0.30 s44.0 cm268 cm/s 0.35 s60.0 cm320 cm/s An Object In Free Fall

16. Free Fall Introduction Section 0 Lecture 1 Slide 16 Lecture 5 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The velocity values steadily increase. –Each point is plotted at the midpoint between the two times. An Object In Free Fall

17. Free Fall Introduction Section 0 Lecture 1 Slide 17 Lecture 5 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The slope of the line is constant. Thus, the acceleration is constant. An Object In Free Fall

18. Free Fall Introduction Section 0 Lecture 1 Slide 18 Lecture 5 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 An Object In Free Fall

19. Free Fall Introduction Section 0 Lecture 1 Slide 19 Lecture 5 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall Other Influence on Dropped Bodies

20. Free Fall Introduction Section 0 Lecture 1 Slide 20 Lecture 5 Slide 20 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The diagram shows the positions at 0.10-sec intervals of a ball moving left to right. Is the ball accelerated? a)Yes. b)No. c)Unable to determine. The ball moves an equal distance during each 0.10-sec interval, so the speed does not change. Thus, the ball is not accelerated.

21. Free Fall Introduction Section 0 Lecture 1 Slide 21 Lecture 5 Slide 21 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The diagram shows the positions at 0.05-sec intervals of two balls moving left to right. Are either or both of these balls accelerated? a)Ball A is accelerated. b)Ball B is accelerated. c)Both balls are accelerated. d)Neither ball is accelerated. Both balls are accelerated. Ball A covers an increasing distance in each 0.05-sec interval, so it is speeding up. Ball B is covering less and less distance with each interval, so it is slowing down. Both of these are accelerations.

22. Free Fall Introduction Section 0 Lecture 1 Slide 22 Lecture 5 Slide 22 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 How does a dropped object behave?  Do two objects behave differently if they have:  different masses?  different shapes?  The feather falls more slowly than the brick.  But what is the REAL reason?

23. Free Fall Introduction Section 0 Lecture 1 Slide 23 Lecture 5 Slide 23 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 5 Free Fall Influence of Gravity

24. Free Fall Introduction Section 0 Lecture 1 Slide 24 Lecture 5 Slide 24 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Tracking a Falling Object How long does it take for the ball to reach the ground? How fast is it traveling when it gets there? –Assuming air resistance effects are small, the ball accelerates at 9.8 m/s 2 ≈ 10 m/s 2. –Each second, its velocity increases by 10 m/s.

25. Free Fall Introduction Section 0 Lecture 1 Slide 25 Lecture 5 Slide 25 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Tracking a Falling Object Starting from rest, its velocity has increased to 10 m/s after the first second; to 20 m/s after 2 s; to 30 m/s after 3 s; etc. –10 m/s > 20 MPH –30 m/s ≈ 70 MPH! During the first second, its average velocity is 10 m/s ÷ 2 = 5 m/s, during which time it travels 5 m. In the first half second, it travels 1.25 m.

26. Free Fall Introduction Section 0 Lecture 1 Slide 26 Lecture 5 Slide 26 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Tracking a Falling Object The distance increases in proportion to the square of the time:

27. Free Fall Introduction Section 0 Lecture 1 Slide 27 Lecture 5 Slide 27 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The Math Approach Let’s put these ideas into math language

28. Free Fall Introduction Section 0 Lecture 1 Slide 28 Lecture 5 Slide 28 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 3 Motion Tossing a Ball

29. Free Fall Introduction Section 0 Lecture 1 Slide 29 Lecture 5 Slide 29 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Throwing a ball downward Let the ball be thrown downward instead of being dropped. –It will have a starting velocity different from zero. –It will reach the ground more rapidly. –It will have a larger velocity when it reaches the ground.

30. Free Fall Introduction Section 0 Lecture 1 Slide 30 Lecture 5 Slide 30 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Beyond Free Fall: Throwing a Ball Upward  What if the ball is thrown upward?  Gravitational acceleration is always directed downward, toward the center of the Earth.  Here, the acceleration is in the opposite direction to the original upward velocity.

31. Free Fall Introduction Section 0 Lecture 1 Slide 31 Lecture 5 Slide 31 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Let the initial velocity be 20 m/s upward. –It immediately starts experiencing a downward acceleration due to gravity, of approximately 10 m/s. –Every second, the velocity decreases by 10 m/s. After 2 s, the ball has reached its highest point. –Its velocity changes direction, from upward to downward, passing through a value of 0 m/s. Now, the downward acceleration increases the downward velocity.

32. Free Fall Introduction Section 0 Lecture 1 Slide 32 Lecture 5 Slide 32 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What is the ball’s acceleration at the top of its path (at t=2 s)? a)zero. b)+10 m/s c)-10 m/s d)+10 m/s 2 e)-10 m/s 2 Gravity does not “turn off” at the top! The ball’s velocity is still changing, as it changes from going up to going down. For a moment the velocity is zero, but the gravitational acceleration is a constant throughout the path.

33. Free Fall Introduction Section 0 Lecture 1 Slide 33 Lecture 5 Slide 33 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The velocity-vs-time plot starts with +20 m/s (upward) at time t=0 and changes at a steady rate of -10 m/s 2 (decreasing 10 m/s each second). Positive velocities correspond to upward motion; negative velocities correspond to downward motion. The slope is constant and negative (for constant downward acceleration).

34. Free Fall Introduction Section 0 Lecture 1 Slide 34 Lecture 5 Slide 34 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology Next Lab/Demo: Forces Thursday 1:30-2:45 ESLC 53 Ch 3 Next Class: Friday 10:30-11:20 BUS 318 room Review Ch 3