# The Universal Law of Gravitation - Sewanhaka High School

The Universal Law of Gravitation Mr.Rockensies Regents Physics A remote force of mutual attraction between any two masses Magnitude of the force depends on the distance between the masses and their size m1

m2 r Distance between the centers Gravity Fg = Gm1m2/r2 Works everywhere for all masses Fg = The force due to gravity m1 and m2 = The masses r = the distance between the center of the two masses G = The Universal gravitation constant = 6.67x10-11Nm2/kg2

G can be found on the front of the reference table Newtons Law of Universal Gravitation The forces due to gravity are small for ordinary objects. In order to see a large noticeable force, there needs to be large scale masses planets, moons, stars, etc. G was measured in a Cavendish Experiment a century after Newton Newtons Universal Law of Gravitation

F F r r2 Inverse Relationship Inverse Square Relationship Relationships

100 kg box rE Earth Fg = (GmEmbox)/rE2 mE = 5.98 x 1024 kg rE = 6.37x106 m both on reference table Fg = (6.67 x 10-11Nm2/kg2)(5.98 x 1024 kg)(100 kg) (6.37x106 m)2 Fg = 983 N same as Fg = mg = 100(9.81) = 981 N Weight Revisited

100 2r E kg Earth Gravity is an inverse-square law Fg 1 r2

Weight off of Earth A question asks you what will happen to the Force of Gravity when the radius between two objects is doubled. How do you find out what will happen? If we multiply r by We multiply Fg by 2 1/22 = 3 1/32 = 1/9 10 1/102 = 1/100

1/()2 = 1/ = 4 So in the example from the previous slide, a 100 kg box 2rE from Earths center weighs 981/22 = 245N What do we do when a question asks Newtons (what we will use) Space around a mass is altered to be a gravitational field. The field exerts a force on a second mass.

M Fg Einstein Space is warped by mass. Traveling in a straight line is impossible. Objects orbit by the following curves in space.

Modern Masses exchange particles (called Bosons) which bind them together. m1 m The Explanations of Gravity

m2 Apparent Weight on an Elevator How does our weight change when we ride in an elevator? Apparent Weight Elevator Free-Body Diagram FN = Fscale

m scale Fg Scales will read normal force, which is the apparent weight 4 cases: 1) Standing still; v = 0, a = 0, FNET = 0

FN = Fg 2) Moving at a constant speed (up or down) a = 0 FNET = 0 FN = Fg 3) Accelerating up, FNET is up therefore FN > Fg scale reads above true weight you feel heavier 4) Accelerating down, FNET is down therefore Fg>FN scale reads below true weight you feel lighter If the elevator is in free fall, FN = 0! Apparent Weight on Incline FN F||

scale F| Fg Scale reads: FN = F | FN = Fgcos always less than Fg

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