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Aristotle’s Laws of Motion 1. Objects in Motion will eventually come to a rest. 2. Heavier objects fall faster than light objects.

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Galileo Showed the Error of the Second Law of Aristotle When dropped, these two different masses will fall with the same acceleration.

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The Error of the First Law was Corrected by Isaac Newton If no external forces act on a moving object, then its motion will continue on without changing.

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Aristotle’s Mistake was in Not Taking Into Account the Effect of Friction An initial push gets this box moving.It eventually comes to a stop. On a frictionless surface such as ice, though, it keeps moving.

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An Object Weighs Less on the Moon 150 lbs! 25 lbs! However, the mass is always the same!

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The More Mass Something Has, the Harder it is to Get Significant Motion. Applied Force Resulting Velocity Same Applied Force Much Lower Resulting Velocity

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Newton’s Second Law of Motion Takes This Into Account If a force F is applied to an object of mass m, a non-zero acceleration a in the direction of the applied force is the result: a = F/m

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If There are More Than Two Forces, They are Added Together as Vectors Force 1 Force 2 Resultant Force due to Force 1 and Force 2 The resultant force is the net force acting on the object. Mass m

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Newton’s Third Law of Motion For every applied force, there also occurs a force of equal magnitude acting in the opposite direction at precisely the same point.

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Newton’s 3 rd Law in Action The force the person exerts on the heavier boulder is equal in magnitude but opposite in direction to the force the boulder exerts on the person--EVEN IF THE BOULDER IS BEING PUSHED UPHILL!!!

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How do we reconcile this? Force of man on boulder Force of boulder on man Force of man on ground Force of ground on man As the man pushes on the ground, the ground responds by pushing on the man. It is this force that pushes both the man and the boulder up the hill!

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The Universal Law of Gravitation

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Near the Earth’s Surface, Gravitational Acceleration is Nearly Constant At sea level, objects accelerate down at a rate of 9.81 m/s 2 At the top of Mt. Everest, objects accelerate down at a rate of 9.78 m/s 2

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The Acceleration Due to Gravity Must Significantly Decrease With Distance If it didn’t the Moon would orbit the Earth once every hour instead of once a month!

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So, What if the Object is Far Away? Acceleration must drop off as you get further from the Earth. By how much does it do so? acceleration < 9.8 m/s 2

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Isaac Newton Figured Out the Force Between Two Masses It made sense to him that as either one (or both) of the masses increases, then the force between both masses would increase. It also made sense to him that the further the separation between the two masses, the less the force between them.

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Newton Had the Information Provided by Johannes Kepler and Tycho Brahe to Help Him Tycho Brahe (1550 - 1605)Johannes Kepler (1575 - 1624)

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Brahe’s Observations and Kepler’s Calculations Showed Planets Orbit the Sun in Ellipses Sun Mars (Ellipse exaggerated for clarity--these orbits are actually almost circular.)

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From the Results of Kepler and Brahe, Newton Used His Own Expectations to Show: The Force due to Gravity is proportional to each mass involved, both m 1 and m 2 The Force due to Gravity is proportional to the SQUARE of the separation between the two masses, r. F = Gm 1 m 2 r2r2 G is the “Gravitational Constant of the Universe”; Newton couldn’t determine its actual value.

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