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Mass Vs. Weight Before we Begin… The Amount of Matter an object has DOES NOT CHANGE Measured in Kg Gravitational attraction of an object to the Earth CHANGES due to LOCATION Measured in Newtons

W = mg W = Fg What is Weight?!? Weight is the force of attraction an object feels due to the gravity of the environment. W = mg Changing the gravity of the environment will change the weight of the object! Weight (Newtons) Mass (kg) Gravity of location (Earth 9.8 m/s2) W = Fg Weight is the FORCE OF GRAVITY

Misconceptions on Measuring Weight FN mg

Weightlessness means =0 FN compensating upward

Law of Universal Gravitation

Distance between two objects. Remember that the distance r corresponds to the distance between the center of gravity of the two objects.

Each mass will exert the SAME force on one another regardless of size.

The Force between any two objects depends on their masses and the distance between them. If the MASS Increases The FORCE Increases If the MASS Decreases The FORCE Decreases If the DISTANCE Increases The FORCE Decreases If the DISTANCE Decreases The FORCE Increases

Both are Fg ? WAIT A MINUTE!!! Fg = G(m1*m2) r2 Fg = mg Works ANYWHERE in the UNIVERSE! Planet Specific (gravity depends on the planet)

Mguy *g Fg = G(mguy*mEarth) r2 g = G * mEarth r2 g = G * mplanet/moon Because of this we can use: To solve for the gravitational pull of Any planet or moon. g = G * mplanet/moon r2

Force Equation – always set it up F= ((G)(m1)(m2)) ((d)2) G is always 6.67 x 10-11

Example F = 2.26 X 1017 N F= G(m1*m2) r2 Calculate the magnitude of the interplanetary force of attraction between Uranus and Neptune. (The mass of Uranus is 8.73 X 1025 kg and the mass of Neptune is 1.03 X 1026 kg) F= G(m1*m2) r2 F = (6.67 x 10-11) (8.73 X 1025)(1.03 X 1026 ) ((1.63 x 1012)2) F = 2.26 X 1017 N

F = ma 6.35x1022 = (8.93 X 1022 )a Example Jupiter Io m= 8.93 X 1022 kilograms Example Jupiter If the gravitational force between Jupiter and Io is 6.35x1022 N, calculate the magnitude of the acceleration of Io due to the gravitational force exerted by Jupiter. F = ma 6.35x1022 = (8.93 X 1022 )a

Inverse Square Law! is any Physical Law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity

You actually weigh less at higher altitudes The Intensity (Pull) you feel from the earth decreases as you move away from the Source (center of the earth) What does that mean?!?! You actually weigh less at higher altitudes

4r 3r 2r r 1 W 1 W 1 W 4 9 16 Inverse Square law Inverse means flipped Source Center of Earth 2r r Inverse means flipped Square is (#)2 W =mg 1 W 1 W 1 W 4 9 16

Law of Gravitation is an Inverse Square law!!!! If something moves twice the distance from earth, their weight will be ¼ of what it was:

Gravity gets weaker as 1/dist2

m = 100kg Fg=(1/9) mg Fg=1088.9 N Fg=(1/4) mg Fg=2450 N Fg= mg 3 Earth Radius Fg=(1/9) mg 2 Earth Radius Fg=1088.9 N Fg=(1/4) mg Fg=2450 N On surface 1 Earth Radius Fg= mg Fg= 9800 N 4 Earth Radius Fg=(1/16) mg Fg=612.5 N

Example An object weighs 100 Newtons on Earth’s surface. When it is moved to a distance that is one Earth radius above Earth’s surface, it will weigh- At 1 radius above the Earth, an object will weigh ¼ of its weight on the surface of the Earth. ¼ of 100N = 25N