What Factors Affect 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 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

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 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?

A Little Perspective

xf = 1/2at2 + vot+ xo

If they are in a frictionless environment, how long would it take for Minnie and Mickey assuming that Mickey

remains motionless.

xf = 1/2at2

a = Fg/m

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

a = 5.5 x 10-8 m/s2

xf = 1/2at2

xf = 0.30 m

t = 3302 s = 55 min

0.30 m

a = Fnet/m

Falling Apples

Newton developed this mathematical relationship.

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

Why are planets different?

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

Fg = maag

Fg =Gmamm

Rm2

maag =Gmamm

Rm2

ag =Gmm

Rm2

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

Comparing GravityJupiter is about 320 x more massive than Earth.

FgE =GmEmO

r2

Jupiter has a radius that is 11 x bigger than Earth.

How does the force of gravity on Jupiter compare to that of Earth?

FgJ =GmJmO

rJ2

Fg =G(320mE)mO

(11rE)2

Comparing Gravity

gJ = 25 m/s2

FgJ =G(320mE)mO

(11rE)2FgJ =

320GmEmO

121rE2

FgJ =GmEmO

rE2

320

121FgJ =

320

121FgE

FgJ = 2.6FgE

gJ = 2.6gE

The Gravitational FieldA vector field is a model that helps us understand

interactions that occur at a distance.

Play with the simulation! Only use blue objects and sensors. Make three observations on your group’s slide!

What Did You Learn??

Period 2 Period 6 Period 8

The Gravitational Field

The gravitational field is always directed toward the mass that creates it.

The gravitational field gets smaller as you move away from the mass that creates it.

The Gravitational Field

The gravitational field is the same strength at all points that are equidistant around a

spherical object

The Gravitational Field

When there are multiple objects, each one will create its own gravitational field. The total

field will be the sum of their individual fields.

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 = Fg

mFg = GmM

r2

g = GMr2

Gravity will get very small with large distances, but is

never zero!

There is no place in the Universe where it is zero!

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 = Fg

mFg = GmM

r2

g = GMr2

Gravity will get very small with large distances, but is

never zero!

There is no place in the Universe where it is zero!

What is Zero Gravity Then?

Zero gravity occurs when an object is accelerating in a way that makes the normal

force disappear.

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 Tides

FEm

FES

FEM =GmmmE

rEM2FES =

GmSmE

rES2

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

Fg = FEM + FES

Remember! You have to add the sign based on your diagram!

The Asteroid Belt

FEm FAJ

FAM =GmAmM

rAM2

FAJ =GmAmJ

rAJ2

Fg = -FAM + FAJ

The net force is zero so they stay where they are in

orbit around the sun!