• What is the centripetal force acting on a 2000 kilogram airplane if it turns with a radius of 1000 meters while moving at 300 meters per second?

ac = v2/r

ac = (300 m/s)2/1000 m

ac = 90 m/s2

Do Now

Fc = mac

Fc = (2000 kg)(90 m/s2)

Fc = 1.8 x 105 N

Aim: How do we solve problems involving gravitation?

Do Now: Quiz

• Attractive force between two objects with mass

• Strength of attraction depends on:– Mass of each object (in kilograms)

– Distance between the objects (in meters)

– Gravitational Constant (G = 6.67 x 10-11 N m∙ 2/kg2)

221

rmGmFg

What is Gravity?

Newton’s Law of Universal Gravitation

m1 m2

R

Fg Fg

Fg = Gm1m2 / R2 (Reference Tables)

3000 m4 x 105 kg

6 x 105 kgF Gm m

rg 1 22

Fg = 1.78 x 10-6 N

Example #1

Practice Problem

• Calculate the gravitational force between the Earth and the Moon. Use your reference tables to determine the mass of the Earth, the mass of the Moon, and the distance between the Earth and the Moon.

Gravitational Proportions

• The force of gravity is DIRECTLY proportional to mass.

• What is the effect on a gravitational system if:• one mass is doubled

GGr

mGmFg 11

)1)(1(22

21 GGr

mGmFg 21

)1)(2(22

21 Base Case

Gravitational Proportions

• The force of gravity is DIRECTLY proportional to mass.

• What is the effect on a gravitational system if:• both masses are doubled

GGr

mGmFg 41

)2)(2(22

21

Gravitational Proportions

• The force of gravity is DIRECTLY proportional to mass.

• What is the effect on a gravitational system if:• one mass is reduced by 1/3

GG

rmGmFg 3

11

)1(31

2221

Gravitational Proportions

• The force of gravity is INVERSELY proportional to the square of distance.

• What is the effect on a gravitational system if:• the distance between masses is doubled

GGr

mGmFg 41

2)1)(1(

2221

Gravitational Proportions

• The force of gravity is INVERSELY proportional to the square of distance.

• What is the effect on a gravitational system if:• the distance between masses is tripled

GGr

mGmFg 91

3)1)(1(

2221

Gravitational Proportions

• The force of gravity is INVERSELY proportional to the square of distance.

• What is the effect on a gravitational system if:• the distance between masses is halved

GGr

mGmFg 4

21

)1)(1(22

21

Exit Ticket

The magnitude of the gravitational force between two objects is 20 newtons. If the mass of each object were doubled, the magnitude of the gravitational force between the objects would be _____newtons.

• Objects with MASS produce gravitational fields

• Field lines point inward from ALL DIRECTIONS

Gravitational Fields

The Gravitational Field

• A gravitational field is a region of space that attracts masses with a gravitational force.

The Gravitational Field

g = Fg / mo

•Units of g are N / kg (same as m / s2)•The gravitational field is simply another way of viewing the action of gravity.•Numerically, the gravitational acceleration and the gravitational field strength are always equal.