The Gravitational Force

What Factors Affect the Gravitational Force?

What Did You Learn?

What is the relationship between F1 and F2?

They are equal in magnitude but opposite in direction.

These forces are a Newton’s Third Law Pair!

What Did You Learn?

What type of relationship is there between Fg and m1?

Proportional!

The gravitational force increases!

What happens as mass 1 increases?

What Did You Learn?

What type of relationship is there between Fg and m2?

Proportional!

The gravitational force increases!

What happens as mass 2 increases?

What Did You Learn?

What type of relationship is there between Fg and m1?

Power!

The gravitational force decreases!

What happens as distance increases?

What Did You Learn?

Does your equation look like this?

Fg = constant * r-2

Fg = constantr2

What does that mean?

Creating a Mathematical Model

Fg = constantr2

Fg = constant * m1

Fg = constant * m2

Fg =constant *m1m2

r2

Because we are talking about gravity, the constant is represented by the letter G!

Fg =Gm1m2

r2

What’s the Attraction?Gravity is known as the weakest of the fundamental forces.

Let’s see how strong it actually is on an everyday level!

What is the force of gravity between a loving couple standing 30 cm apart

if one has a mass of 60 kg and the other has a mass of 75 kg?

Fg =Gm1m2

r2

Fg = 3.3 x 10-6 N

If the dance floor is frictionless, how long would it take them to reach each other?

What’s the Attraction?

xf = 1/2at2 + vot+ xo

If the dance floor is frictionless, how long would it take them to reach each other?

xf = 1/2at2

a = F/m

Minnie: a = 3.3 x 10-6 N/60 kg

Mickey: a = 3.3 x 10-6 N/75 kg

a = 5.5 x 10-8 m/s2

a = 4.4 x 10-8 m/s2

xf = 1/2at2 + 1/2at2

xf = 0.30 m

t = 2462 s = 41 min

Falling Apples

Newton developed this mathematical relationship.

A falling apple is experiencing the same force as the moon orbiting the Earth!

What is G?A scientist named Cavendish was trying to figure

out the internal structure of the Earth.

Designed an experiment to determine the Earth’s mass.

G = 6.67 x 10-11 Nm2/kg2

Weighing the Earth

Let’s say you have an apple in free fall.

Fg = maag

Fg =GmamE

r2

maag =GmamE

r2

ag =GmE

r2

Weighing the EarthIf the apple is near the Earth’s surface, then the distance

between the apple and the Earth is the Earth’s radius.

ag =GmE

r2

mE =r2ag

G

Units must be in kg, m, and s!

mE = 5.96 x 1024 kg mE = 5.98 x 1024 kg

What’s the Free fall Acceleration?Jupiter’s moon, Io, has a mass of 8.93 x 1022 kg and has a

diameter of 3630 km. What is the acceleration due to gravity on an object in free fall at Io’s surface?

ag =GmI

r2

Info:

ag = 1.8 m/s2

mI = 8.93 x 1022 kg

r = 1,815,000 m mo = ?

ag = ?

moag =GmImO

r2

The Gravitational FieldThe gravitational field at any point in space is defined as the

gravitational force felt by a tiny unit mass placed at that point.

g is known as the gravitational field. The magnitude of g is…

g = Fm

g = GMr2

Multiple ForcesObjects can experience multiple forces of gravity at once.

The tides are caused by the gravitational pull of the

Moon on the Earth.

Spring tides occur twice a lunar month and are caused when the Earth, Moon, and Sun are all aligned.

It is important to remember that the gravitational equation only gives you the magnitude of the force!

You will need a free-body diagram to determine the direction!

Spring TidesmE = 5.98 x 1024 kg

mM = 7.35 x 1022 kg

mS = 1.99 x 1030 kg

rES = 149.6 million km

rEM = 384,400 kmFEm

FES

FEM =GmmmE

rEM2FES =

GmSmE

rES2

The gravity equation can only look at two objects at a time!

Fg = FEM + FES

Fg = 1.98 x 1020 N + 3.54 x 1022 N = 3.56 x 1022 N

Unit 4C - Problem Set

Topic Sections Questions

Force of Gravity 4.7 20, 23, 24, 25, 28

Uniform Circular Motion 5.1-5.3 1, 2, 13, 19, 23

Satellites and Orbits 5.5 & 5.6 32, 36

Vertical Circular Motion 5.7 42, 45, 60

Things To Remember When Completing Your Problem Set!

A picture can illustrate the situation or be a free-body diagram!