1. Center of Gravity and Stability of an Object
Mrs. Kummer
Spring 2016

2. Learning Intentions By the end of the lesson we will be able to…
Understand the term Center of Mass/Gravity (CoG)
Recognize the factors that affect an object’s CoG
Investigate how to find the CoG of an irregular object.

3. Center of Gravity
This is the point at which the whole weight of the body can be taken as acting through or
the point from which the object will balance
Metre rule each, there are three different edges that is possible to balance the rule on. Try to find out what they are and balance the rule on each of the edges. If an imaginary line was to be marked vertically along each of the axis that the ruler was balanced on, where would the exact point be that all three line crossed? This is the point where the ruler’s Center of Gravity is located.

4. Regular and uniform objects
The geometrical Center of some common shapes-
This is also where the Center of gravity and the object’s weight, W, can be considered to act
Mark on where the Center of the shape is for the three shapes shown. W W W

5. For a triangle
The Center of gravity (and geometrical Center) is found by drawing a line from the corner to the opposite line’s midpoint
Attempt to find the Center of the triangles shown W W W

6. For non-uniform shapes
When more than one material makes up an object the Center of gravity will be affected.
Try finding the Center of gravity of the tube
Why has the CoG changed?
Check out the bird balancing on its beak!

7. External CoG
For some objects the CoG is not located on the actual object -
Stool
Again draw the object and mark on their Center
Explain how and why the CoG would change if the bottom plank was twice as dense as the other plank… roughly mark the new CoG
Ring
2 uniform perpendicular planks W W W

8. Why does the object balance?
Linked to Principle of Moments
When the object is suspended from a point it will come to rest when the clockwise moment is equal to the anti clockwise moment
Anti- Clockwise Moment = Clockwise Moment
The Humble metre rule

9. Icebergs!
Lake Tasman where the terminal merrain of the Tasman glacier is located in NZ, South Island close to Mount Cook in McKenzie country. The end of the glacier has large chunks of ice that randomly break away and float in the lake. This is ice is thousands of years old as it has slowly inched its way down the Tasman valley to finally end its journey in the lake.

10. As these guys melt their CoG changes and they roll over!
The water lapping against the iceberg melts the edges and also the Sun’s energy changes the shape of the mass. The iceberg will have to tilt or turn over slightly to re-balance itself and the underside of the iceberg becomes visible when this happens. The surface and colour of the underside is very different from the stained, sun-beaten exposed side.

11. The smooth deep blue colour is partially transparent and it is possible to see the pieces of rock suspended in the iceberg which the glacier would have ripped from the sides of the valley as it rubbed up against the edges.

12. Learning Intentions By the end of the lesson we will be able to…
Understand the term Center of Mass/Gravity (CoG)
Recognize the factors that affect an object’s CoG
Investigate how to find the CoG of an irregular object.

13. When an object is suspended
When an object is suspended, so that it can swing freely, it will come to rest with its CoG vertically below the point of suspension
See Page 52 and 53 for extra notes in the book

14. CoG of an irregular shape
Find the CoG of an irregular shaped lamina
Pin held by clamp b c a a b c c b a
hole
plumb line

15. Balancing Act! Now, try to balance the object at that point…
Question- explain in terms of moments why the object can be balanced at this point? c a b
Answer- on one side of the point of CoG, the object’s weight is causing a turning effect. This is counter balanced on the other side where the weight is causing a turning effect in the opposite direction.

16. Example
1 m long spade balances in a string loop when the loop is 30 cm from the end of the blade.
A 2 kg mass is placed at the handle and the balance point is at the Center of the spade.
What is the mass of the spade?
Ans 5 kg
2 kg

17. Learning Intentions By the end of the lesson we will be able to…
Recall how the stability of an object depends on the…
position of the Center of gravity
size of the object’s base

18. Put these in order of STABILITY3 4
Back of the book – order of stability, give a reason why! 2 1
Position of Center of Gravity

19. Stability
An object will be in STABLE EQUILIBRIUM when it returns to its original position after given a small displacement
Buskers’ festival – they love to show off how great their stability is…

20. Page 53 Neutral Equilibrium Unstable Equilibrium
Put the cones in order of stability (come back to why they are in that order in a few slides time!)
Why does the drinking bird alternate between being stable and toppling over? Can you explain this in term of moments, the turning effect of a force? Where is the pivot, what is the force causing the turning?
As soon as the ‘weight’ is concentrated more in the bird’s head he then becomes unstable and topples over.
A turning effect of a force/moment is needed to cause the object to rotate.
Why does the can roll up hill? The CoG acts vertically down, but if it acts outside the object’s base then it will cause the object to rotate in that direction, i.e. the can moves up hill due to the extra 100 g mass which changes where its CoG’s location is.
The same is true for the bird. The bird’s CoG has in fact moved up and over. Once it acts outside the base of the bird, he tips over.

21. Rotates Anti-Clockwise
Stability
For an object to start rotating it needs to have an unbalanced moment acting on it-
Rotates Clockwise
Rotates Anti-Clockwise
Check out the weebles- also masters of stability, impossible to topple over!
Pivot
Pivot W W W
Stable
Stable
Unstable

22. Back to the starting activity
An object becomes unstable when its Center of Gravity falls outside of the object’s base.
Why?
All of the object’s weight can be considered as acting through the CoG. If this acts outside the base then it will cause a turning effect or a moment

23. The Traffic Cone A great example of a VERY stable object.
What features of the cone make it so stable?
Low Center of Gravity
Wide base

24. Balance and Sport
Board sports require stability and a low CoG. The CoG is continually shifting to direct the board and the rider. The back needs to be kept straight while the hips, knees and ankles provide all the turning. The head too needs to be kept still and in line with the core so that it doesn’t cause any unbalance. As soon as the CoG acts outside the area of the board, the rider is in danger of losing control.

25. Balance and Sport
Rock climbing too relies on the body’s position and the potential turning effect of the body’s weight. Whenever a hand-hold is used as a pivot, the body’s CoG will need to be shifted closer to the hold before the climber’s fatigue cause them to let go. The body needs to be flexible to quickly position itself and reduce the size of the turning effect.

26. Balance and Sport
Some of the World’s greatest footballers, fantastic dribblers with close control and nearly impossible to topple over due to their low CoG. Pocket rockets who are small yet unstoppable because they have such precise balance.

27. The Double Decker Bus
Each of the diagrams on the right represent a Double Decker bus with passengers inside.
Draw out and label the one which shows all passengers on
the lower level
the upper level
both levels

28. Delete a word to complete the sentences
If more people sit upstairs on the bus the CoG will rise/fall. This will make the bus more stable/unstable and it can be tilted by a greater/lesser angle
The bus will fall over when the CoG acts inside/outside of the bus’ base
A stable object has a low/high CoG and a narrow/wide base

29. Question Time
Who’s stronger: Guys or Girls????
Let’s find out!