1. 4/21 & 4/22
Do Now – TAKE ONE
Don’t forget your HW for tonight!!! Read & Study 10.1, 10.4, 10.6 Complete #1-3, 8-10, (p. 147)
10 points!!!

2. Center of Mass
The center of mass of an object is the point located at the object’s average position of mass. (CM)
The center of gravity of an object is the point located at the object’s average position of weight. (CG)
**For this course, we can use the terms Center of Gravity [CG] and Center of Mass [CM] interchangeably in most scenarios**

3. Location of the Center of Mass
For a symmetrical object, such as a baseball, the center of mass is at the geometric center of the object.
For an irregularly shaped object, such as a baseball bat, the center of mass is toward the heavier end.

4. 11.3 Center of Mass
The center of mass for each object is shown by the red dot.

5. Center of Mass
The centers of mass of the baseball and of the spinning baseball bat each follow parabolic paths…
All objects thrown in the air will rotate about their CG in this way

6. Center of Mass
As an object slides across a surface, its center of mass follows a straight-line path.
If the wrench were tossed into the air, its center of mass would follow a smooth parabola.

7. Center of Mass
Objects not made of the same material throughout may have the center of mass quite far from the geometric center.
Consider a hollow ball half filled with lead. The center of mass would be located somewhere within the lead part.
The ball will always roll to a stop with its center of mass as low as possible.

8. Locating the Center of Gravity
The center of gravity (CG) of a uniform object is at the midpoint, its geometric center.
The CG is the balance point.
Supporting that single point supports the whole object.

9. Center of Gravity
The weight of the entire stick behaves as if it were concentrated at its center. The small vectors represent the force of gravity along the meter stick, which combine into a resultant force that acts at the CG.

10. Center of Gravity
The weight of the entire stick behaves as if it were concentrated at its center. The small vectors represent the force of gravity along the meter stick, which combine into a resultant force that acts at the CG.

11. Center of Gravity
The CG of an object may be located where no actual material exists.
The CG of a ring lies at the geometric center where no matter exists.
The same holds true for a hollow sphere such as a basketball.

12. Center of Gravity of People
The center of gravity of a person is not located in a fixed place, but depends on body orientation.

13. Center of Gravity of People
When you stand straight up with your arms hanging at your sides, your CG is within your body, typically 2 to 3 cm below your navel, and midway between your front and back.
Raise your arms vertically overhead. Your CG rises 5 to 8 cm.
Bend your body into a U or C shape and your CG may be located outside your body altogether.

14. Center of Gravity of People
A high jumper executes a “Fosbury flop” to clear the bar while his CG nearly passes beneath the bar.

15. Center of Gravity
think!
Can an object have more than one CG?

16. Center of Gravity think! Can an object have more than one CG? Answer:
Yes & No
No more than one CG at a time…BUT the location of an object’s CG can change!
A rigid object has one CG.
If a non rigid object, such as a piece of clay or putty (or a person!) is distorted into different shapes, then its CG may change as its shape is changed.
Even then, it has one CG for any given shape.

17. B & C WILL topple A will NOT topple
THE RULE FOR TOPPLING
(back of your paper)
If the center of gravity of an object is DIRECTLY ABOVE the area of support, the object will remain upright.
B & C
WILL
topple
A will NOT topple

18. will NOT topple will NOT topple WILL topple
THE RULE FOR TOPPLING
The block topples when the CG extends beyond its support base.
will NOT topple
will NOT topple
WILL
topple

19. will NOT topple THE RULE FOR TOPPLING
The Leaning Tower of Pisa does not topple over because its CG lies above its base.
will NOT topple

20. AREA OF SUPPORT
The support base of an object does not have to be solid. An object will remain upright if the CG is VERTICALLY above its base of support.
The shaded area bounded by the bottom of the chair legs defines the support base of the chair.
When you stand, your CG is somewhere above the area bounded by your feet.

21. Center of Gravity of People
When you stand, your CG is somewhere above your support base, the area bounded by your feet.
In unstable situations, as in standing in the aisle of a bumpy-riding bus, you place your feet farther apart to increase this area.
Standing on one foot greatly decreases this area.

22. Video Questions (PBS VIDEO – Center of Gravity ) http://www. pbs

23. A DAY - Today’s Goals Finish #1-4 Complete #5-6 as a class
Complete #7-9 in groups of your choosing
Check in at stop sign
Finish all of the activities in your POGIL, leaving 7 minutes before the bell.

24. B DAY - Today’s Goals
Finish #1-4

25. B DAY - Today’s Goals
Finish #1-4
Complete #5-6
as a class

26. B DAY - Today’s Goals Finish #1-4 Complete #5-6 as a class

27. 7.
We don’t know exactly WHERE it is…just that it is ABOVE the area of support!

28. 8.
IN other words…
Its CG is NOT above its area of support!

29. 9.
IN other words…
Its CG is above its area of support!

30. Station 2: CHAIR LIFT Let’s have a contest, boys vs. girls!
Challenge a member of the opposite sex to compete in this activity with you.
Stand EXACTLY 2 foot lengths away from a wall.
Place a chair between yourself and the wall
Bend over with a straight back (so that your back is perfectly parallel with the floor, and perpendicular to the wall), and let your head lean against the wall
KEEP YOUR HEAD AGAINST THE WALL and lift the chair off the floor.
Then, attempt to straighten up.
2. FIVE minutes to complete the station and #16
***HINT – READ P. 145!!!!

31. Station 2: CHAIR LIFT
Who has a LOWER CG?
Girls
Boys
Same

32. Station 3: Wall Stand
Stand with the back of your feet directly against a wall. Do not bend your knees, and try to touch your toes.
1. FOUR minutes to complete the station and the questions!!

33. Center of Gravity of People
You can lean over and touch your toes without toppling only if your CG is above the area bounded by your feet.

35. Station 5: Tippy Toes
Stand facing a wall with your toes against the wall. Place your nose against the wall and stand on your tip toes.
1. FOUR minutes to complete the station and the questions!

37. GO BACK & FINISH… Station 1: Sit on a chair Station 4: Meter Stick
CHECK IN AT STOP SIGNS!!!

38. EXIT SLIP Complete and turn in Don’t forget your HW for tonight
EXIT SLIP Complete and turn in Don’t forget your HW for tonight!!! Read & Study 10.1, 10.4, 10.6 Complete #1-3, 8-10, (p. 147)