Chapter 10 Center of Gravity
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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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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

A hammer behaves a little differently


An object naturally spins around its:

center of mass

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

center of gravity


Center of Gravity or Center of Mass

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

CM


If an object is symmetrical and

uniform (made of the same material throughout)

the center of mass is just the center

CM


If an object has more mass at one end,

the center of mass if shifted that way

CM

Lead

Plastic





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


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


CM

A massive sun and 3 small planets.

Where is the center of mass?

Sun


Sun

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


Sun

The sun actually wobbles a bit because…



Compare the center of mass after the explosion? constant?

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



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

Where is the center of mass


If a puck is pushed across a frictionless table sometimes but not others?

It moves in a straight line at a constant speed


A motion graph for this is… sometimes but not others?


If a wrench is slid across a frictionless table sometimes but not others?

The wrench below spins about is CM

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




But really just 2 things happen path

1.) the object rotates around its CM

2.) the CM follows a parabolic path


If ball is thrown into the air, it follows a parabolic path path(sorry can’t control the speed any better)


The hammer does 2 things when tossed path

1.) rotates around the CM

2.) the CM follows the typical path




The center of mass / center of gravity path

is special for several reasons.


FOR EXAMPLE: path

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

Fg

BUT this would make calculations a bit tiresome


FOR EXAMPLE: path

Fg = mg

BUT you can PRETEND like the Force of gravity

is only pulling down on the CENTER OF MASS


F pathN = mg

Fg = mg

When a fulcrum is placed under the CM,

It balances!!!

(the net force is zero)






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

What would happen to the CM?

Would it still balance?



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

Are in line with gravity, it will balance


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)


Why doesn’t the leaning tower of pisa fall? is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.


Would the object at the right fall over is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

?


Would the object at the right fall over is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

YES

Fg

Fg

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


This block can’t be tilted anymore without falling is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

Fg


DEMO- Tilting box is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.


The CM is still under the base is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

Still a little sinking left before TIMBER!!!


A bus MUST withstand an angle of 28 is hung by a point with a plum bob attached. The line will ALWAYS run through the CM. o without tipping

Some can withstand 40o

28o

Center line

40o


The CM must be lower for a greater tipping angle is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

Highest CM for 28o

Highest CM for 40o


How do the manufacturers get the CM well below the is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

halfway mark, even with passengers on the top deck?

Highest CM for 40o


Cargo in the back of truck should always be secured is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

OK


If it isn’t secured or strapped in then… is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

OK

UH OH


Activity: is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

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


physics is hung by a point with a plum bob attached. The line will ALWAYS run through the CM.

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



This is more stable for 2 reasons happens to the CM?

#1 a lower CG

Which is more stable


The object at right must have its CM go UP before falling happens to the CM?

The object at left does not


Unstable happens to the CM? equilibrium

Stable equilibrium

Any movement lowers the CM

The CM must rise first


physics happens to the CM?

physics

physics

If the book is more stable here

Why does it not fall when upright?


CM animation happens to the CM?


The object is forced to pivot at the fulcrum. happens to the CM?

Any rotation causes the CM to rise

Stable equilibrium


What about like this? happens to the CM?

UNstable equilibrium


What about here? happens to the CM?

This object is in neutral equilibrium..

The CM doesn’t rise or fall as it rotates


Equal mass L/R & U/D happens to the CM?

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


Book questions happens to the CM?

page 147

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


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