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Balanced Rock Arches National Park Moab, Utah It doesn’t seem stable why doesn’t it fall? Chapter 10 Center of Gravity

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When a ball is spun in the air it spins around its center & so does a block of wood A hammer behaves a little differently That is to say the axis of rotation is through the center of the object

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An object naturally spins around its: center of mass which is very similar to (we will use these interchangeably) center of gravity

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Center of Gravity or Center of Mass This is a location of the average position of mass in an object CM

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If an object is symmetrical and uniform (made of the same material throughout) the center of mass is just the center CM

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If an object has more mass at one end, the center of mass if shifted that way CM Lead Plastic

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Where is the center of mass?

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Where would the CM of a large pot be?

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But you can’t just say that there is the same amount of mass to the left and to the right Geometric center shown at line At what point would there be the same mass to the left & right (assume the string is massless) Where do you think this set of masses connected by a string would rotate about if swung in the air Equal mass L/R & U/D Actual CM 1 kg 2 kg

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Actual CM 1 kg 2 kg 1 m Multiply the mass times its distance from the center of mass 2 m * 1 kg1 m * 2 kg

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Sun A massive sun and 3 small planets. Where is the center of mass? CM

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

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The sun actually wobbles a bit because… Sun

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Does the center of mass of our solar system change or is it constant? Sun

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Compare the center of mass after the explosion? If there are no outside forces, the center of mass is the same

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What if the fragments are different sizes?

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Why does a washing machine vibrate during the spin cycle sometimes but not others? Where is the center of mass

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If a puck is pushed across a frictionless table It moves in a straight line at a constant speed

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A motion graph for this is…

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The wrench below spins about is CM If a wrench is slid across a frictionless table And its CM moves in a straight line at a constant speed

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If a baseball is thrown into the air it follows a parabolic path

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If a bat is tossed it looks a little more chaotic but….

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But really just 2 things happen 1.) the object rotates around its CM 2.) the CM follows a parabolic path

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

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The hammer does 2 things when tossed 1.) rotates around the CM 2.) the CM follows the typical path

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Now at the same time.

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A hammer thrown into the air

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The center of mass / center of gravity is special for several reasons.

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Gravity pulls down on an entire meter stick (each atom) FOR EXAMPLE: BUT this would make calculations a bit tiresome Fg

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FOR EXAMPLE: BUT you can PRETEND like the Force of gravity is only pulling down on the CENTER OF MASS F g = mg

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When a fulcrum is placed under the CM, It balances!!! F g = mg F N = mg (the net force is zero)

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This is an easy way to find the center of mass of an object JUST BALANCE IT ON YOUR FINGER

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If a weight is hung at one end, what happens to the CM

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So the object isn’t balanced

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In order to be balanced the pivot must be in line with the CM

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What if the mass was dropped down by a string? What would happen to the CM? Would it still balance?

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LET’s Try it

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As long as the CM of mass and the pivot point Are in line with gravity, it will balance

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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)

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Why doesn’t the leaning tower of pisa fall?

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Would the object at the right fall over ?

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

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FgFg This block can’t be tilted anymore without falling

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DEMO- Tilting box

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The CM is still under the base Still a little sinking left before TIMBER!!!

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A bus MUST withstand an angle of 28 o without tipping Some can withstand 40 o Center line 28 o 40 o

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The CM must be lower for a greater tipping angle Highest CM for 28 o Highest CM for 40 o

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How do the manufacturers get the CM well below the halfway mark, even with passengers on the top deck? Highest CM for 40 o

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Cargo in the back of truck should always be secured OK

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If it isn’t secured or strapped in then… OK UH OH

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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

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Where is the book most stable physics A system is most stable with the CM as low as possible. There is a tendency towards this state. Demo: rolling concrete

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If a ping pong ball is pushed into the water in a glass what happens to the CM?

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Which is more stable This is more stable for 2 reasons #1 a lower CG

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The object at right must have its CM go UP before falling The object at left does not

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Unstable equilibrium Stable equilibrium Any movement lowers the CM The CM must rise first

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If the book is more stable here physics Why does it not fall when upright? physics

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CM animation

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The object is forced to pivot at the fulcrum. Any rotation causes the CM to rise Stable equilibrium

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What about like this? UNstable equilibrium

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What about here? This object is in neutral equilibrium.. The CM doesn’t rise or fall as it rotates

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But you can’t just say that there is the same amount of mass to the left and to the right Geometric center shown at line At what point would there be the same mass to the left & right (assume the string is massless) Where do you think this set of masses connected by a string would rotate about if swung in the air Equal mass L/R & U/D Actual CM

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Book questions page 147 9, 12, 14, 17, 18, 19, 23, 24, 26

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