Physics Section 3.2 Free Fall

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1 Physics Section 3.2 Free Fall

2 Aristotle Aristotle taught that the substances making up the Earth were different from the substance making up the heavens. He also taught that dynamics (the branch of physics that deals with motion) was primarily determined by the nature of the substance that was moving.

3 Galilei Galileo 1600 s Studied how things fell Didn t have a good clock Rolled balls down an inclined plane Found that the speed increased as it rolled down the ramp 1st person to explain acceleration of moving objects and falling bodies.

4 Galilei Galileo t = 0 t = 1 second t = 2 seconds t = 3 seconds

5 Galileo Free Fall Acceleration Due to the Earth s Gravity When dropped, these two different masses will fall with the same acceleration!

6 Free Fall - Falling Objects Free Fall When gravity is the only force acting on an object (free fall acceleration) is directed toward the center of the earth. For free fall, it is customary to use the letter g to represent the acceleration because the acceleration is due to gravity. Although g varies slightly in different parts of the world, its average value is nearly 9.81 m/s 2 or 32 ft/s 2. (These numbers are important, remember them!)

7 Free Fall - Falling Objects Since the acceleration of gravity is a constant of 9.81 m/s 2, this means the speed of a falling object increases by 9.81 m/s every second. Thinker: What does it means if you were on the moon and the acceleration due to gravity is 1.62 m/s 2?

8 Free Fall All objects fall at the same rate If you drop a coin and a feather at the same time you will notice that the coin reaches the ground way before the feather. Why??? However, if you were to take the air out of the container (vacuum) you would find that the coin and feather fall together and hit the bottom at the same time!

9 Free Fall Air Resistance In Air: A stone falls faster than a feather Air resistance affects stone less In a Vacuum: A stone and a feather will fall at the same speed.

10 Videos

11 Free Fall The constant acceleration of an object moving only under the force of gravity is "g". The acceleration caused by gravity is 9.81 m/s 2 or 32 ft/s 2. If there was no air (Vacuum), all objects would fall at the same speed Doesn t depend on mass

12 Values of g in different places There are various different values of g. Since g is due to the attraction of the earth, it will decrease as we get farther from the earth s center. Acceleration due to gravity is smaller at higher elevations Acceleration due to gravity is larger at a higher latitude City Elevation above Sea Level Latitude G (m/s 2 ) Washington DC 8 m 38⁰ 54 N Denver 1,640 m 39⁰ 43 N London 30 m 51⁰ 30 N Therefore; 9.81 m/s 2 is an average figure. This value includes effects due to the earth s rotation and the value excludes effects due to air resistance. So, we will treat all free falling bodies as undergoing constant acceleration.

13 Values of g in different places Acceleration due to gravity is smaller at higher elevations Acceleration due to gravity is larger at a higher latitude

14 Terminal Velocity You can assume that a = g = 9.81 m/s 2 for speeds up to several meters per second. The resistance from air friction increases as a falling object s speed increases. Eventually, the rate of acceleration is reduced to zero and the object falls with constant speed. The maximum speed at which an object falls when limited by air friction is called the terminal velocity.

15 Terminal Velocity

16 Since acceleration is a vector and vectors must have magnitude and direction we will always use the following system in our acceleration problems with gravity: Y-Axis Initial Motion is always positive (+) from reference point. (The reference point is the point where the object has stated its movement) Opposite Direction of Initial Motion is always negative (-) from reference point

17 Since acceleration is a vector and vectors must have magnitude and direction we will always use the following system in our acceleration problems with gravity: X-Axis Direction of movement is positive (+) Gravity g = ± 9.81 m/s 2 or ± 32 ft/s 2 (Depending on units and reference point direction)

18 Acceleration as a Vector

19 A pebble dropped from a bridge The vector is oriented down

20 A baseball tossed up in the air, halfway up the path The vector is oriented down

21 A baseball tossed up in the air, at the top The vector is oriented down.

22 A baseball tossed up in the air, right before it strikes the ground The vector is oriented down.

23 A football is thrown at a 45º angle, at the top of its path The vector is oriented down.

24 A cannonball rolling off a table The vector is oriented down.

25 Example #1 A body falls freely from rest. Find: a. Its acceleration b. The distance it falls in 3 s c. Its speed after falling 70 m d. The time required to reach a speed of 25 m/s

26 Example #2 A stone falls from rest from a fourth-floor window that is 14 meters above ground level. a. How long does it take to reach the ground? b. What is the velocity just before it strikes the ground?

27 Example #3 A stone is thrown vertically upward with a velocity of 10 m/s from a fourth-floor window 14 meters above ground level. What is the velocity just before striking the ground?

28 Example #4 A ball dropped from a bridge strikes the water in 5 seconds. Neglecting air resistance, find: a. The speed with which it strikes the water b. The height of the bridge

29 Example #5 A stone is thrown vertically upward with a velocity 40 m/s at the edge of a cliff having a height of 110 m. Neglecting air resistance, what is the velocity when the stone strikes the ground?

30 Example #6 A ball is thrown vertically downward from the edge of a high cliff with an initial velocity of 25 ft/s. a. How fast is it moving after 1.5 s? b. How far has it moved after 1.5 s?

31 Aristotle The Dynamics of Aristotle For example, stripped to its essentials, Aristotle believed that a stone fell to the ground because the stone and the ground were similar in substance (in terms of the 4 basic elements, they were mostly "earth"). Likewise, smoke rose away from the Earth because in terms of the 4 basic elements it was primarily air (and some fire), and therefore the smoke wished to be closer to air and further away from earth and water. By the same token, Aristotle held that the more perfect substance (the "quintessence") that made up the heavens had as its nature to execute perfect (that is, uniform circular) motion. He also believed that objects only moved as long as they were pushed. Thus, objects on the Earth stopped moving once applied forces were removed, and the heavenly spheres only moved because of the action of the Prime Mover, who continually applied the force to the outer spheres that turned the entire heavens. (A notorious problem for the Aristotelian view was why arrows shot from a bow continued to fly through the air after they had left the bow and the string was no longer applying force to them. Elaborate explanations were hatched; for example, it was proposed that the arrow creating a vacuum behind it into which air rushed and applied a force to the back of the arrow!)

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