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**The Universal Law of Gravitation**

Mr.Rockensies Regents Physics

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**Gravity r 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 Gravity Distance between the centers

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**Newton’s Law of Universal Gravitation**

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 = 6.67x10-11N·m2/kg2 G can be found on the front of the reference table Newton’s Law of Universal Gravitation

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**The forces due to gravity are small for ordinary objects**

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 Newton’s Universal Law of Gravitation

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F F r2 r Inverse Relationship Inverse Square Relationship Relationships

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**Weight Revisited 100 kg box Fg = (GmEmbox)/rE2 mE = 5.98 x 1024 kg rE**

rE = 6.37x106 m both on reference table rE Earth Fg = (6.67 x 10-11N•m2/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

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**Weight off of Earth 2rE Gravity is an inverse-square law Fg α 1 r2**

100 kg Earth Fg α 1 r2 Weight off of Earth

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**What do we do when a question asks…**

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… /22 = ¼ /32 = 1/9 /102 = 1/100 ½ /(½)2 = 1/¼ = 4 So in the example from the previous slide, a 100 kg box 2rE from Earth’s center weighs 981/22 = 245N What do we do when a question asks…

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**The Explanations of Gravity**

Newton’s (what we will use) Space around a mass is altered to be a gravitational field. The field exerts a force on a second mass. 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. M Fg m1 m2 m The Explanations of Gravity

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**How does our weight change when we ride in an elevator?**

Apparent Weight on an Elevator How does our weight change when we ride in an elevator?

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Apparent Weight Scales will read normal force, which is the “apparent weight” Free-Body Diagram Elevator FN = Fscale m scale Fg

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4 cases: 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 Accelerating up, FNET is up therefore FN > Fg scale reads above true weight – you feel heavier 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!

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**Apparent Weight on Incline**

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

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