The Universal Law of GravitationMr.Rockensies

Regents Physics

Gravity

• 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

rDistance between the centers

Newton’s Law of Universal Gravitation

Fg = Gm1m2/r2

Works everywhere for all massesFg = The force due to gravitym1 and m2 = The massesr = the distance between the center of the two massesG = The Universal gravitation constant = 6.67x10-11N·m2/kg2

G can be found on the front of the reference table

• 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

Relationships

F F

r2 r

Inverse Relationship Inverse Square Relationship

Weight Revisited

rE

Earth

100 kg box Fg = (GmEmbox)/rE2

mE = 5.98 x 1024 kgrE = 6.37x106 mboth on reference table

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 off of Earth

Earth

2r E 100 kg

Gravity is an inverse-square law

Fg α 1 r2

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 = ¼3 1/32 = 1/910 1/102 = 1/100½ 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

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.

EinsteinSpace is warped by mass. Traveling in a straight line is impossible. Objects orbit by the following curves in space.

ModernMasses exchange particles (called Bosons) which bind them together.

m1 m2M Fg

m

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

Apparent Weight on an Elevator

Apparent WeightScales will read normal

force, which is the “apparent weight”

scale

Elevator

m

FN = Fscale

Fg

Free-Body Diagram

4 cases:1) Standing still; v = 0, a = 0,

FNET = 0 FN = Fg

2) Moving at a constant speed (up or down) a = 0FNET = 0 FN = Fg

3) Accelerating up, FNET is up therefore FN > Fg

scale reads above true weight – you feel heavier4) 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

θ

scale

F |

Fg

FN

F||

Scale reads: FN = FFN = Fgcosθ always less than Fg

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