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Gravity and Free Fall

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Gravity Sir Isaac Newton ( ) developed a law of gravitation which said all objects in the universe attract each other through gravitational force Universal Gravitation Equation F = G m1m2 d 2 Equation shows grav. Force ↑ as both masses ↑ Equation shows grav. Force ↓ as the distance b/w masses ↑

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Free Fall Free fall- when gravity is the only force acting on an object (free fall acceleration is directed toward center of earth) The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s 2. Galileo found that all things fall at the same rate in the absence of air resistance, regardless of their mass

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Free Fall The rate of falling increases by 9.8 m/s every second. Height = ½ gt 2 For example: ½ (9.8 )1 2 = 4.9 m ½(9.8)2 2 = 19.6 m ½ (9.8)3 2 = 44.1 m ½ (9.8)4 2 = 78.4 m

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Air Resistance In air… –A stone falls faster than a feather Air resistance affects stone less In a vacuum –A stone and a feather will fall at the same speed.

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Mass and Weight different! intrinsic property environment ► Mass is an intrinsic property of an object. It is completely determined by the number and type of atoms that make up the object. It does not depend on the environment in which the object is located. ► But weight is different. Weight depends on both the object itself, and on some other object that exerts the gravitational force. So, for example, the mass of an object would be the same on the moon or the Earth; but the weight would be different.

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What does weight depend on? The weight of an object depends on the object’s mass. –In fact, an object’s weight is directly proportional to the object’s mass. The weight of an object also depends on the object’s location. –In fact, an object’s weight is directly proportional to its free fall acceleration, g at its current location.

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Weight = the force of gravity The weight of an object is, by definition, the strength of the force of gravity pulling the object downward. force of gravity W = m g newtons kg

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Weight of a 1 kg object Since W = mg, the weight of a 1 kg object is: –W = (9.8 m/s 2 )(1 kg) = 9.8 N on Earth –W = (1.6 m/s 2 )(1 kg) = 1.6 N on the Moon

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Mass vs. Weight Mass is not Weight Weight is a force - an interaction between 2 objects involving a push or a pull. One of these objects is typically VERY big - the Earth or the Moon, for instance. Weight is NOT a property of an object

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Weight In symbols: W = mg W m g

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Gravity What is the force acting on the mass m due to the Earth’s gravity? If released, the acceleration of m would be … By Newton’s second law the force on m must be … By the way, what is the reaction force? Solution That is, the magnitude, or strength, is mg and the direction is downward. g = 9.81 m/s 2 F

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2-5. Free Fall A ball thrown horizontally will fall at the same rate as a ball dropped directly.

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2-5. Free Fall A ball thrown into the air will slow down, stop, and then begin to fall with the acceleration due to gravity. When it passes the thrower, it will be traveling at the same rate at which it was thrown.

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Example. Playing catch with a softball The trajectory has 3 parts. the throw the catch free fall What is the force acting on the ball, during each part of the trajectory?

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Projectile Motion An object thrown upward at an angle to the ground follows a curved path called a parabola. combines vertical and horizontal motion Orbiting objects- forward motion combines with free fall and object follows a curved path

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2-6. Air Resistance Free Fall stops accelerating –A person in free fall reaches a terminal velocity of around 54 m/s which means the person stops accelerating b/c: –Force of air resistance = gravitational force –Called terminal velocity (balanced forces) –With a parachute, terminal velocity is only 6.3 m/s Allows a safe landing

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Free Fall Review Dropping something from a resting position (gains speed as it falls so it accelerates) Gravity pulls objects down (air resistance can affect how fast) (no air resistance- in a vacuum) When gravity is the only thing that affects falling object → FREE FALL Acceleration due to gravity is 9.8 m/s 2

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Free Fall equations V = g x t D = 1 gt 2 2

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