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Balanced Rock Arches National Park Moab, Utah

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Chapter 10 Center of Gravity. It doesn’t seem stable why doesn’t it fall?. Balanced Rock Arches National Park Moab, Utah. When a ball is spun in the air it spins around its center & so does a block of wood. That is to say the axis of rotation is through the center of the object.

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Presentation Transcript
slide1
Chapter 10 Center of Gravity

It doesn’t seem stable why doesn’t it fall?

Balanced Rock

Arches National Park

Moab, Utah

slide2
When a ball is spun in the air it spins around its center

& so does a block of wood

That is to say the axis of rotation is through the center of the object

A hammer behaves a little differently

slide3
An object naturally spins around its:

center of mass

which is very similar to (we will use these interchangeably)

center of gravity

slide4
Center of Gravity or Center of Mass

This is a location of the average position of mass in an object

CM

slide5
If an object is symmetrical and

uniform (made of the same material throughout)

the center of mass is just the center

CM

slide6
If an object has more mass at one end,

the center of mass if shifted that way

CM

Lead

Plastic

slide10
Equal mass L/R & U/D

Actual CM

But you can’t just say that there is the same amount of mass to the left and to the right

Where do you think this set of masses connected by a string would rotate about if swung in the air

At what point would there be the same mass to the left & right (assume the string is massless)

1 kg

2 kg

Geometric center shown at line

slide11
2 m * 1 kg

1 m * 2 kg

Multiply the mass times its distance from the center of mass

Actual CM

1 kg

2 kg

1 m

1 m

1 m

slide12
CM

A massive sun and 3 small planets.

Where is the center of mass?

Sun

slide13
Sun

The solar system does NOT rotate around the center of the sun.

slide14
Sun

The sun actually wobbles a bit because…

slide16
Compare the center of mass after the explosion?

If there are no outside forces, the center of mass is the same

slide18
Why does a washing machine vibrate during the spin cycle sometimes but not others?

Where is the center of mass

slide19
If a puck is pushed across a frictionless table

It moves in a straight line at a constant speed

slide21
If a wrench is slid across a frictionless table

The wrench below spins about is CM

And its CM moves in a straight line at a constant speed

slide24
But really just 2 things happen

1.) the object rotates around its CM

2.) the CM follows a parabolic path

slide25
If ball is thrown into the air, it follows a parabolic path (sorry can’t control the speed any better)
slide26
The hammer does 2 things when tossed

1.) rotates around the CM

2.) the CM follows the typical path

slide30
The center of mass / center of gravity

is special for several reasons.

slide31
FOR EXAMPLE:

Gravity pulls down on an entire meter stick (each atom)

Fg

BUT this would make calculations a bit tiresome

slide32
FOR EXAMPLE:

Fg = mg

BUT you can PRETEND like the Force of gravity

is only pulling down on the CENTER OF MASS

slide33
FN = mg

Fg = mg

When a fulcrum is placed under the CM,

It balances!!!

(the net force is zero)

slide38
What if the mass was dropped down by a string?

What would happen to the CM?

Would it still balance?

slide40
As long as the CM of mass and the pivot point

Are in line with gravity, it will balance

slide41
Another interesting fact about the CM, it that if an object is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

A Gravity Vector drawn from the pivot point will always pass through the CM (when balanced)

slide44
Would the object at the right fall over

YES

Fg

Fg

An object will topple if a vertical line through its CG is not under the support base

slide47
The CM is still under the base

Still a little sinking left before TIMBER!!!

slide50
A bus MUST withstand an angle of 28o without tipping

Some can withstand 40o

28o

Center line

40o

slide51
The CM must be lower for a greater tipping angle

Highest CM for 28o

Highest CM for 40o

slide52
How do the manufacturers get the CM well below the

halfway mark, even with passengers on the top deck?

Highest CM for 40o

slide56
Activity:

Place your feet on the floor in front of you chair.

Now stand up BUT notice what you do before standing!!!

Demos: balanced boards

hammer paint stick

slide57
physics

physics

Where is the book most stable

A system is most stable with the CM as low as possible.

There is a tendency towards this state.

Demo: rolling concrete

slide59
This is more stable for 2 reasons

#1 a lower CG

Which is more stable

slide61
Unstable equilibrium

Stable equilibrium

Any movement lowers the CM

The CM must rise first

slide62
physics

physics

physics

If the book is more stable here

Why does it not fall when upright?

slide66
The object is forced to pivot at the fulcrum.

Any rotation causes the CM to rise

Stable equilibrium

slide67
What about like this?

UNstable equilibrium

slide68
What about here?

This object is in neutral equilibrium..

The CM doesn’t rise or fall as it rotates

slide69
Equal mass L/R & U/D

Actual CM

But you can’t just say that there is the same amount of mass to the left and to the right

Where do you think this set of masses connected by a string would rotate about if swung in the air

At what point would there be the same mass to the left & right (assume the string is massless)

Geometric center shown at line

slide70
Book questions

page 147

9, 12, 14, 17, 18, 19, 23, 24, 26

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