The Universal Law of Gravitation Mr.Rockensies Regents Physics

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

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

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

F F r2 r Inverse Relationship Inverse Square Relationship Relationships

Weight Revisited 100 kg box Start with equation: Fg = (GmEmbox)/rE2 Givens: mE = 5.98 x 1024 kg 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

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

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… 2 1/22 = ¼ 3 1/32 = 1/9 10 1/102 = 1/100 ½ 1/(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…

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

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?

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

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!

Apparent Weight on Incline FN F|| scale F | θ Fg Scale reads: FN = F FN = Fgcosθ always less than Fg |