GravitationGravitation

Learning Goal 7.2 (part 1): Compare and contrast gravitational fields and electric fields.

Learning Goal 7.3: Quantitatively describe the gravitational interaction between two objects.

Confession Time…Confession Time…I’m attracted to my calculator.The closer I am to my calculator,

the more attracted I am.Whether you admit it or not, you’re

attracted to my calculator too.And my calculator is attracted to

you, too…The fact is, EVERYTHING is

attracted to EVERYTHING ELSE… at least gravitationally.

Wait, Really?Wait, Really?Yes! EVERY object exerts a

gravitational force on EVERY other object… not just planets and stars, but buildings and people and office supplies as well.

Gravitation InvestigationGravitation InvestigationResearch question: How do

mass and distance affect the gravitational force two objects exert upon one another?

Gravitational FieldsGravitational FieldsA field is a region in which a

force is felt at a distance; when we draw a field, we show what the force vector would look like at a variety of positions.

A gravitational field looks like…

Gravitational ForceGravitational ForceThe strength of the gravitational force

exerted on an object depends on mass and distance.

Gravitational force and mass have a linear relationship.◦m x 2 Fg x 2 m x 3 Fg x 3

Gravitational force and distance have an inverse square relationship.◦d x 2 Fg x 1/4 d x 3 Fg x 1/9

Universal Law of Universal Law of GravitationGravitation

Fg = gravitational force (N)G = constant of universal

gravitation (Nm²/kg²)m1 = mass of object 1 (kg)m2 = mass of object 2 (kg)r = distance between the

two objects (m)G = 6.67 x10-11

Nm²/kg²

A Couple Things to Note…A Couple Things to Note…This is the SAME force of gravity

that we dealt with earlier; for objects on Earth’s surface, we just simplified:

where

A Couple Things to Note…A Couple Things to Note…If you want your sweetie pie to

be more attracted to you, all you have to do is

(1) get closer together, and (2) gain lots of weight.

Sample ProblemSample ProblemA 90 kg person stands 1.5 m

from a 60 kg person sitting on a bench nearby. How strong is the gravitational force between them?

m1 = 90 kgm2 = 60 kgr = 1.5 mG = 6.67 x10-11 Nm²/kg²Fg = ?

Fg = (6.67 x10-11)(90)(60) (1.5²)

Fg = 1.6 x 10-7 N…… itty bitty force!

Sample ProblemSample ProblemA student standing on the surface of

Mars weighs 261 N. Given that Mars has a mass of 6.42 x 1023 kg and a radius of 3,390 km, what is the student’s mass? How much would the student weigh on Earth?Fg, Mars = 261 N

m1 = 6.42 x 1023 kgr = 3390 km = 3.39 x 106 mG = 6.67 x10-11 Nm²/kg²m2 = ?

261 = (6.67 x10-11)(6.42 x 1023)(m2) (3.39 x 106)²

m2 = 70 kg

Fg, Earth = mg = (70 kg)(9.8 m/s2)

Fg, Earth = 686 N

Fun Fact: OrbitFun Fact: OrbitWhen an object orbits, the

gravitational force perfectly matches the centripetal force necessary to keep the object in uniform circular motion.

That means that if YOU threw an object fast enough, YOU could put that object into orbit. Unfortunately, “fast enough” means about 8000 m/s. (For comparison, a bullet fired from a gun travels at about 900 m/s.)