1. Air Resistance (R) and Terminal Velocity (v T ) … No need to copy anything yet—just Follow Along!

3. Drag Equation: F d = ½  v 2 C d A At NTP (normal Temperature and Pressure: 20 o C, 1atm): What is the density of air?????? Guess in teams.

4. Drag Equation: F d = ½  v 2 C d A At NTP (normal Temperature and Pressure: 20 o C, 1atm): What is the density of air?????? Guess in teams.  = 1.20kg/m 3 (engineeringtoolbox.com)engineeringtoolbox.com Copy Drag equation and value of air density at NTP in Big Ideas.

5. Drag Equation: F d = ½  v 2 C d A Imagine Car 1 driving at 10mph. Car 1: F d = ½  (10mph) 2 C d A = 100mph 2 * other factors.

6. Drag Equation: F d = ½  v 2 C d A Imagine Car 1 driving at 10mph. Car 1: F d = ½  (10mph) 2 C d A = 100mph 2 * other factors. Imagine identical Car 2 driving at 20mph: Car 2: F d = ½  (20mph) 2 C d A

7. Drag Equation: F d = ½  v 2 C d A Imagine Car 1 driving at 10mph. Car 1: F d = ½  (10mph) 2 C d A = 100mph 2 * other factors. Imagine identical Car 2 driving at 20mph: Car 2: F d = ½  (20mph) 2 C d A = 400mph 2 * other factors. Imagine identical Car 2 driving at 20mph: Car 2: F d = ½  (30mph) 2 C d A

8. Drag Equation: F d = ½  v 2 C d A Imagine Car 1 driving at 10mph. Car 1: F d = ½  (10mph) 2 C d A = 100mph 2 * other factors. Imagine identical Car 2 driving at 20mph: Car 2: F d = ½  (20mph) 2 C d A = 400mph 2 * other factors. Imagine identical Car 2 driving at 20mph: Car 2: F d = ½  (30mph) 2 C d A = 900mph 2 * other factors.

9. Car and airplane designers work hard to minimize C d ’s. Why? http://en.wikipedia.org/wiki/Automobile_drag_coefficient http://ecomodder.com/wiki/index.php/Vehicle_Coefficient_of_Drag_List http://en.wikipedia.org/wiki/Automobile_drag_coefficient http://ecomodder.com/wiki/index.php/Vehicle_Coefficient_of_Drag_List

10. http://en.wikipedia.org/wiki/Drag_coefficient

11. From http://www.50by30.org/transportation/transportation-examples/transportation-examples-manitoba Drag without aerodynamic enhancements. http://www.50by30.org/transportation/transportation-examples/transportation-examples-manitoba Improving Truck Efficiency Drag with aerodynamic enhancements

12. Drag Equation: F d = ½  v 2 C d A Problem #1: How do you expect the C d for 1 and 2 coffee filters to compare? Write a sentence.

13. Drag Equation: F d = ½  v 2 C d A Problem #1: How do you expect the C d for 1 and 2 coffee filters to compare? Write a sentence. What do you know abut F d when filters fall at v T ? Hint: Draw FBD of filter.

14. Drag Equation: F d = ½  v 2 C d A Problem #1: How do you expect the C d for 1 and 2 coffee filters to compare? Write a sentence. What do you know abut F d when filters fall at v T ? Hint: Draw FBD of filter. F d = W. What info to you need to find the drag coeffs?

15. Drag Equation: F d = ½  v 2 C d A Problem #1: How do you expect the C d for 1 and 2 coffee filters to compare? Write a sentence. What do you know abut F d when filters fall at v T ? Hint: Draw FBD of filter. F d = W. What info to you need to find the drag coeffs? A  ______ (what units?) Mass of 1 filter = _________

16. Drag Equation: F d = ½  v 2 C d A Problem #1: How do you expect the C d for 1 and 2 coffee filters to compare? Write a sentence. What do you know abut F d when filters fall at v T ? Hint: Draw FBD of filter. F d = W. What info to you need to find the drag coeffs? A  ______ (what units?) Mass of 1 filter = _________ Find the 2 coefficients of drag! How was your prediction?????

17. Drag Equation: F d = ½  v 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball..

18. Drag Equation: F d = ½  v 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ?.

19. Drag Equation: F d = ½  v 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W!.

20. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W!.

21. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W! What information to you need i/o solve this?.

22. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W! What information to you need i/o solve this? Ping Pong ballSteel ball m: diam: C d :.

23. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W! What information to you need i/o solve this? Ping Pong ballSteel ball m: 2.1g241g diam: 3.9cm3.9cm C d : Nasa: www.grc.nasa.gov/WWW/k-12/airplane/shaped.htmlwww.grc.nasa.gov/WWW/k-12/airplane/shaped.html Wikip: en.wikipedia.org/wiki/Drag_coefficienten.wikipedia.org/wiki/Drag_coefficient Engineeringtoolbox: http://www.engineeringtoolbox.com/drag-coefficient-d_627.html http://www.engineeringtoolbox.com/drag-coefficient-d_627.html.

24. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W! What information to you need i/o solve this? Ping Pong ballSteel ball m: 2.1g241g diam: 3.9cm3.9cm C d : Let’s use 0.10 for both spheres. Nasa: www.grc.nasa.gov/WWW/k-12/airplane/shaped.htmlwww.grc.nasa.gov/WWW/k-12/airplane/shaped.html Wikip: en.wikipedia.org/wiki/Drag_coefficienten.wikipedia.org/wiki/Drag_coefficient Engineeringtoolbox: http://www.engineeringtoolbox.com/drag-coefficient-d_627.html http://www.engineeringtoolbox.com/drag-coefficient-d_627.html.

25. to solve for v T : W = ½  v T 2 C d A Problem #2: Find the terminal velocities of the steel ball and of the ping pong ball. What do we know about F d at v T ? F d = W! What information to you need i/o solve this? Ping Pong ballSteel ball m: 2.1g241g diam: 3.9cm3.9cm C d : Let’s use 0.10 for both spheres. Nasa: www.grc.nasa.gov/WWW/k-12/airplane/shaped.htmlwww.grc.nasa.gov/WWW/k-12/airplane/shaped.html Wikip: en.wikipedia.org/wiki/Drag_coefficienten.wikipedia.org/wiki/Drag_coefficient Engineeringtoolbox: http://www.engineeringtoolbox.com/drag-coefficient-d_627.html http://www.engineeringtoolbox.com/drag-coefficient-d_627.html That’s it: find the terminal velocities!!!!!

26. How did you do? Compare your results to some terminal velocities of other objects: http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html

27. Air resistance, F d, is fairly negligible (<10% of weight) for solid, baseball size objects or larger, moving < 10m/s. (no need to copy yet!)

28. Post-Lab Objectives: i.ID factors that determine the time it takes an object to reach ground; ii.ID factors that affect air resistance (F d ); when does F d need to be considered? iii.Understand why terminal velocity (v T )occurs, and compare v T for various objects

29. Conclusions from Falling Objects Lab  A falling object has only two forces acting on it: weight and air resistance. These forces, along with the object’s mass, determine its motion.  When air resistance (F d ) is fairly negligible compared to W (which is true for solid, baseball size objects or larger, moving < 10m/s):  acceleration on Earth is: a  g  9.81m/s/s  the time the object takes to reach the ground depends only on its initial velocity, initial height, and g.

30. Homework! 1.Find the C d for a 150-lb skydiver, whose terminal velocity is 125mph. Assume a projected area of 0.95m 2. 2.Find the terminal velocity of a baseball. m = 145g r = 3.66cm C d = 0.52