1. Free Fall J. Frank Dobie H.S.

2. Free Fall Free-falling object falling falls only under the influence of gravity. Free-falling object is “in a state of free fall.” Two important characteristics: 1. Free-falling objects do not encounter air resistance. 2. All free-falling objects on Earth accelerate downwards at a rate of 9.81 m/s 2.

3. 1. 1. Free falling objects fall only under the influence of what ? Free falling objects fall only under the influence of gravity.

4. 2. What does an acceleration of -9.81 m/s 2 really mean? Every second the object is increasing its velocity 9.81 m/s downward.

5. 3. What is the direction of the acceleration during free fall? Free fall is acceleration that is directed downward.

6. 4. What is absent when an object is undergoing free fall? Air resistance is absent during free fall.

7. 5. Is an object thrown upward undergoing free fall? Yes, any object released in the air is undergoing free fall.

8. 6. If an object is thrown downward, is it undergoing free fall? An object thrown downward is undergoing free fall.

9. *Free-falling objects are accelerating downwards at a rate of 9.81m/s 2. *A ticker tape trace of it motion is a model that depicts the acceleration. * The diagram at the right shows the ticker tape trace that shows the position every 0.1 second. *The distance the ball travels every interval of time is increasing is a sign that the ball is speeding up as it falls downward. *The acceleration is directed downward in the same direction the speed is increasing.

10. 7. What is the value of the acceleration due to gravity? The acceleration due to gravity is -9.81m/s 2.

11. Acceleration of Gravity The acceleration of a free-falling object is so important that it is known as the acceleration of gravity. * Physicists have a special symbol to denote it --- the symbol g. * The numerical value for the acceleration of gravity is most accurately known as 9.81 m/s 2. * We will use 10m/s 2 during conceptual understanding of the acceleration.

12. 8. What is the symbol for the acceleration due to gravity? The symbol for the acceleration due to gravity is g.

13. 9. Does the acceleration due to gravity change at your location on the earth? The acceleration due to gravity does not change at a particular location on the earth.

14. Velocity and Time Pattern A velocity and time table for a free-falling object being dropped from rest would look like the following: Time(s) Velocity(m/s), downward 0 0 1 10 2 20 3 30 4 40 5 50 Remember, the acceleration of 10m/s 2 causes the velocity to increase 10 m/s per s.

15. Speed Pattern during Free Fall Assuming that the position of a free-falling ball dropped from a position of rest is shown every 1 second, the speed of the ball will be shown to increase as depicted in the diagram at the right. (This diagram is not drawn to scale.)

16. 10. If you follow the pattern for the speed during free fall when an object is released from rest : 10 m/s, 20 m/s, what would be the next two values for the speed? The next two values for the speed would be 30 m/s and 40 m/s.

17. Representing Free Fall by Graphs Position vs. Time Graphs for free-falling objects Observe that the line is curved. A curved line on a position vs. time graph signifies an accelerated motion: 10 m/s 2

18. A closer look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). The negative slope of the line indicates a negative (downward) velocity.

19. 11. What does the position vs. time graph for free fall from rest look like?

20. 12. What does the negative slope on a position vs. time graph for an object undergoing free fall indicate? The negative slope on a position vs. time graph for an object undergoing free fall indicates the object is undergoing a downward velocity.

21. Velocity vs. Time Graphs The velocity vs. time graph for a free- falling object is shown below. Observe that the line on the graph is a straight, diagonal line which signifies an accelerated motion.

22. A closer look at the velocity-time graph reveals that the object starts with a zero velocity and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. Analysis of the slope is -10 m/s 2 or more accurately -9.81 m/s 2.

23. 13. What does the velocity vs. time graph look like for an object released from rest and undergoes free fall?

24. 14.What does the slope of a velocity vs. time graph for free fall represent? The slope of a velocity vs. time graph for free fall represents the acceleration of gravity (-9.81 m/s 2 ).

25. How Fast? and How Far? Free-falling objects are in a state of acceleration. *How Fast? The speed is dependent upon the length of time for which it has fallen. v f = v i + gt Ex: If t = 5 s v f = 10 m/s 2 (5 s) = 50 m/s

26. 15. What is the velocity of an object moving after released from rest for 8 s? v f = v i + at 0 + -10 m/s 2 (8s) -80 m/s

27. 16.What is the velocity of an object undergoing free fall from rest for 10 s? v f = v i + at V f = 0 + -10 m/s 2 (10s) V f = -100 m/s

28. How Far? * The distance a free-falling object falls depends upon the time of fall. x = v i (t) + ½ a t 2 Ex: v i = 0 m/s and t = 1 s x = ½ (10 m/s 2 ) (1s) 2 = 5 m The diagram shows the results of several distance calculations For a free-falling object dropped from a position of rest.

29. 17. How far does a stone fall in 3 s from rest? x = v i t + ½ at 2 x = 0(3s) + ½ (-10 m/s 2 ) (3s) 2 x = -45 m………45 m

30. 18. What is the displacement for an object that falls freely for 8.0 s? x = v i t + ½ a t 2 X = 0 t + ½ (-10. m/s 2 ) (8.0s) 2 -320 m

31. The Big Misconception “Doesn’t a massive object accelerate at a greater rate than a less massive object?” Nearly everyone has observed the difference in rate of fall of a single piece of paper and a textbook.

32. The answer to the question “ Doesn’t a massive object accelerate at a greater rate than a less massive object?” is …absolutely not! That is, absolutely not, if you are considering the specific type of falling motion know as free-fall. Free-falling object do not encounter air resistance. Massive objects will only fall faster than less massive objects if there is an appreciable amount of air resistance present.

33. The Big Answer The explanation of why all objects accelerate at the same rate involves the concepts of force and mass. You will learn that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. All objects, regardless of their mass, free- fall at the same rate of acceleration.

34. 19. Why does a hammer and feather hit the ground at the same time on the moon? A hammer and feather hit the ground at the same time on the moon because there is very little air resistance on the moon.

35. 20.Does a massive object accelerate at a greater rate than a less massive object when there is an absence of air resistance? A heavy object will accelerate at the same rate as a less massive object when there is an absence of air resistance.

36. Definition for Free Fall Object falling only influence of gravity Air Resistance is ignored. Under such conditions, all objects will fall with the same rate of acceleration, regardless of their mass.all objects will fall with the same rate of acceleration, regardless of their mass

37. Falling with Air Resistance Object falling through air usually encounter some degree of air resistance. Air resistance results from collisions of the object’s leading surface with air molecules Actual amount of resistance depends on various factors--- speed of object and cross-sectional area of the object. *Increased speeds result in increased amount of air resistance. *Increased cross-sectional areas result in increased amount of air resistance.

38. Terminal Velocity Objects which encounters air resistance eventually reach a terminal velocity. As an object falls, it picks up speed, which increases air resistance. The force of air resistance becomes large enough to balance the force of gravity. The object has now reached terminal velocity where it no longer increases in speed.

39. When there is air resistance, more massive objects fall faster than less massive objects. Consider the objects below of different masses: A falling object will continue to accelerate to higher speeds until they encounter an amount of air resistance equal to their weight.

40. Since the 150-kg skydiver weighs more (experiences a greater force of gravity), it will accelerate to higher speeds before reaching a terminal velocity. More massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity. More massive objects accelerate to higher speeds until the air resistance force equals the gravity force.